6,186 results
Search Results
2. On Modeling Viral Diffusion in Heterogeneous Wireless Networks
- Author
-
Nguyen, Hoai-Nam, Shinoda, Yoichi, Akan, Ozgur, Series editor, Bellavista, Paolo, Series editor, Cao, Jiannong, Series editor, Dressler, Falko, Series editor, Ferrari, Domenico, Series editor, Gerla, Mario, Series editor, Kobayashi, Hisashi, Series editor, Palazzo, Sergio, Series editor, Sahni, Sartaj, Series editor, Shen, Xuemin (Sherman), Series editor, Stan, Mircea, Series editor, Xiaohua, Jia, Series editor, Zomaya, Albert, Series editor, Coulson, Geoffrey, Series editor, Schmidt, Andreas U., editor, and Lian, Shiguo, editor
- Published
- 2009
- Full Text
- View/download PDF
3. COVID-19 and India: what next?
- Author
-
Behl, Ramesh and Mishra, Manit
- Published
- 2021
- Full Text
- View/download PDF
4. Forecasting the impact of epidemic outbreaks on the supply chain: modelling asymptomatic cases of the COVID-19 pandemic.
- Author
-
Jha, Pradeep K., Ghorai, Suvadip, Jha, Rakhi, Datt, Rajul, Sulapu, Gowrishankar, and Singh, Surya Prakash
- Subjects
COVID-19 pandemic ,BASIC reproduction number ,COVID-19 ,VIRAL transmission ,EPIDEMICS ,PRECISION farming - Abstract
An epidemic outbreak largely disrupts supply chains (SCs) worldwide through plummeting business confidence, especially when it becomes a pandemic; its unpredictable re-emergence and spreadability may lead to inappropriate decision-making, in turn causing severe economic shocks. In March 2020, the coronavirus disease 2019 (COVID-19) outbreak attained a pandemic level, and many millions of cases were confirmed globally. Many countries reported an increasing number of active cases and formulated long-term lockdown guidelines, which resulted in an unexpected disruption of SCs. A key challenge in this scenario is that the rising number of confirmed COVID-19 cases does not necessarily reflect the already infected or asymptomatic cases. It is thus critical to understand the impact of asymptomatic carriers on the SC, as they may be the key driver of the novel virus spread, disrupting long-term SCs. This paper generalised the susceptible-exposed-infected-recovered (S-E-I-R) approach to create a mathematical model for which the impact of a proposed asymptomatic situation on the SC is evaluated through the basic reproduction number (R
0 ), considered the main driver of SC disruption and the equilibrium status of infection over time. This paper presents an action plan for reducing disruption in the SC based on the R0 of the model. Overall, the current study as validated through a case study suggests that the asymptomatic-situation-based model is more convenient for critically understanding as well as forecasting the outbreak’s impact on SCs. This study also highlights different perspectives of SCs for managing such types of pandemics using modelling approaches. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
5. New Challenges in the Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-Pharmaceutical Actions and Vaccination Strategies.
- Author
-
Verrelli, Cristiano Maria and Della Rossa, Fabio
- Subjects
COVID-19 pandemic ,MATHEMATICAL models ,VACCINATION ,BASIC reproduction number ,SARS-CoV-2 Omicron variant - Abstract
This document discusses the challenges faced in mathematical modeling and controlling COVID-19 epidemics. It highlights the global impact of the pandemic on the economy and health, as well as the uneven effects on different age groups. The availability of vaccines led to mass vaccination campaigns, prompting researchers to implement new strategies and innovative approaches. The document also mentions various journals that have published special issues on COVID-19, covering topics such as forecasting, vaccination strategies, and control measures. The special issue presented in this document consists of eleven papers that analyze clinical characteristics, variant spread, economic recovery, mortality rates, non-pharmaceutical interventions, and coordinated actions. The papers propose mathematical models and control strategies to minimize disease spread and prioritize vaccination. The document emphasizes the multidisciplinary nature of the research, involving fields such as applied mathematics, data science, engineering, biology, and economics. Overall, this special issue provides valuable insights into the mathematical modeling and control of COVID-19 epidemics. [Extracted from the article]
- Published
- 2024
- Full Text
- View/download PDF
6. Dynamical analysis of a spatio-temporal model encompassing the avian flu transmission in human population.
- Author
-
Hariharan, S., Shangerganesh, L., and Kumar, Sunil
- Abstract
Unidentified diseases are becoming more prevalent among humans due to various climatic factors, and some of these diseases originate in animals before spreading to humans. One virus that has been of particular concern is the avian influenza virus, which primarily infects bird and can subsequently transmit to humans. This article presents a mathematical model describing the spatio-temporal reaction-diffusion process involved in the transmission of avian flu in human population. The paper begins by studying the proposed model's well-posedness and the calculated basic reproduction number, which provides valuable insights into the dynamics of virus transmission. The paper also provides stability analysis for the disease-free steady state of the model. All theoretical studies are validated using computational results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
7. Dynamics of a linear source epidemic system with diffusion and media impact.
- Author
-
Li, Wenjie, Zhao, Weiran, Cao, Jinde, and Huang, Lihong
- Subjects
BASIC reproduction number ,EPIDEMICS ,LINEAR systems ,LYAPUNOV functions - Abstract
This paper studies an impact of media epidemic system with diffusion and linear source. We first derive the uniform bounds of solutions to impact on media reaction diffusion system. Then, the basic reproduction number is calculated and the threshold dynamics of impact media reaction diffusion system is also given and the Kuratowski measure κ of non-compactness is also considered. In addition, assume the spatial environment is homogeneous, it is shown that the unique endemic equilibrium of the system is global stability by constructing suitable Lyapunov function. Finally, we discuss the asymptotic profile of the system when the diffusion rate of the susceptible (infected) individuals for the system tends to zero or infinity. The main results show that the activities of infected individuals can only be at low risk, and then the virus eventually will be extinct, that is, to control the entry of viruses from abroad and increase the detection of domestic viruses. Finally, some numerical simulations are worked out to confirm the results obtained in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
8. A fractional‐order model of coronavirus disease 2019 (COVID‐19) with governmental action and individual reaction
- Author
-
Jaouad Danane, Zakia Hammouch, Karam Allali, Saima Rashid, and Jagdev Singh
- Subjects
78a70 ,Risk awareness ,2019-20 coronavirus outbreak ,Special Issue Papers ,Coronavirus disease 2019 (COVID-19) ,basic infection reproduction number ,General Mathematics ,Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ,General Engineering ,34a08 ,Fractional calculus ,37n25 ,Caputo fractional‐order derivative ,sensitivity analysis ,Action (philosophy) ,COVID‐19 ,Order (exchange) ,numerical simulation ,Special Issue Paper ,Econometrics ,26a33 ,Basic reproduction number ,Mathematics - Abstract
The deadly coronavirus disease 2019 (COVID-19) has recently affected each corner of the world. Many governments of different countries have imposed strict measures in order to reduce the severity of the infection. In this present paper, we will study a mathematical model describing COVID-19 dynamics taking into account the government action and the individuals reaction. To this end, we will suggest a system of seven fractional deferential equations (FDEs) that describe the interaction between the classical susceptible, exposed, infectious, and removed (SEIR) individuals along with the government action and individual reaction involvement. Both human-to-human and zoonotic transmissions are considered in the model. The well-posedness of the FDEs model is established in terms of existence, positivity, and boundedness. The basic reproduction number (BRN) is found via the new generation matrix method. Different numerical simulations were carried out by taking into account real reported data from Wuhan, China. It was shown that the governmental action and the individuals' risk awareness reduce effectively the infection spread. Moreover, it was established that with the fractional derivative, the infection converges more quickly to its steady state.
- Published
- 2021
9. Dynamic analysis and optimal control of knowledge diffusion model in regional innovation ecosystem under digitalization.
- Author
-
He, Zitong, Wang, Haijun, Hu, Yuhan, Ma, Xiaolin, and Zhao, Huiyan
- Subjects
DIGITAL technology ,DIFFUSION of innovations ,DIFFUSION control ,DIGITAL communications ,BASIC reproduction number ,ECOSYSTEMS ,AUTODIDACTICISM - Abstract
Knowledge diffusion in regional innovation ecosystems is an important factor that influences the regional innovation efficiency. In regional innovation ecosystems under digital empowerment, the knowledge diffusion enables the optimal allocation of innovation resources and promotes the sustainable development and ecological evolution of regional innovation ecosystems. In this paper, a SEIR (Susceptible–Exposed–Infected–Recovered) model is proposed for knowledge diffusion in regional innovation ecosystems under digitization. The basic reproduction number of the proposed model is calculated and its stability is validated. Finally, the expressions for the optimal control system and the optimal control parameters are presented. According to the research conclusions of this paper, the knowledge-diffusion ability of innovation agents in an innovation ecosystem affects the knowledge diffusion in a system; the contact rate between innovation agents affects the efficiency of knowledge diffusion in the system and the structure of the system; the digital transmission ability of innovation agents affects the breadth of knowledge diffusion in the system; and the self-learning ability of innovation agents affects the efficiency of knowledge diffusion in the system.The digital technologies help heterogeneous innovation agents in regional innovation ecosystems to break down the knowledge silos. At the same time, the digital technologies enhance the ability of innovation agents to absorb and learn knowledge in regional innovation ecosystems under digitization, thereby increasing the infection rate of knowledge diffusion in such systems.These conclusions extend the theoretical boundaries of innovation ecosystems and knowledge diffusion and offer management implications for enterprises and governments in decision-making. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
10. Mathematical analysis of an SIQR model with non-linear incidence and saturated treatment rates.
- Author
-
Yadavt, Sudha, Bhadauria, Archana Singh, and Verma, Vijai Shanker
- Subjects
MATHEMATICAL analysis ,COMMUNICABLE diseases ,DISEASE management ,MEDICAL screening ,BASIC reproduction number ,INTERVENTION (Federal government) ,EMERGING infectious diseases - Abstract
Today, because infectious diseases have a large impact on people, control methods for all infectious diseases are crucial. In this paper, we propose a SIQR model with Crowley-Martin type incidence rate and saturated treatment. We have incorporated precautionary measures taken by the population through the saturated incidence rate. Screening of individuals who have come into contact with infected individuals is modelled. Thus, we explore a four-dimensional mathematical model to study the dynamics of the infectious diseases and their management. Stability and bifurcation analysis ofthe system is done. The Mensitivity analysis of all parameters in relation to the basic reproduction number has been performed and the theoretical results have been validated using numerical simulation. Mathematical results in this paper suggest that both government interventions and individual efforts must be incorporated to achieve better control of emerging infectious diseases in the population. [ABSTRACT FROM AUTHOR]
- Published
- 2024
11. SIRS Epidemic Models with Delays, Partial and Temporary Immunity and Vaccination.
- Author
-
Chen-Charpentier, Benito
- Subjects
EPIDEMICS ,COMMUNICABLE diseases ,INFLUENZA epidemiology ,MATHEMATICAL models ,DIFFERENTIAL equations - Abstract
The basic reproduction, or reproductive number, is a useful index that indicates whether or not there will be an epidemic. However, it is also very important to determine whether an epidemic will eventually decrease and disappear or persist as an endemic. Different infectious diseases have different behaviors and mathematical models used to simulated them should capture the most important processes; however, the models also involve simplifications. Influenza epidemics are usually short-lived and can be modeled with ordinary differential equations without considering demographics. Delays such as the infection time can change the behavior of the solutions. The same is true if there is permanent or temporary immunity, or complete or partial immunity. Vaccination, isolation and the use of antivirals can also change the outcome. In this paper, we introduce several new models and use them to find the effects of all the above factors paying special attention to whether the model can represent an infectious process that eventually disappears. We determine the equilibrium solutions and establish the stability of the disease-free equilibrium using various methods. We also show that many models of influenza or other epidemics with a short duration do not have solutions with a disappearing epidemic. The main objective of the paper is to introduce different ways of modeling immunity in epidemic models. Several scenarios with different immunities are studied since a person may not be re-infected because he/she has total or partial immunity or because there were no close contacts. We show that some relatively small changes, such as in the vaccination rate, can significantly change the dynamics; for example, the existence and number of the disease-free equilibria. We also illustrate that while introducing delays makes the models more realistic, the dynamics have the same qualitative behavior. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
12. Dynamics analysis of a reaction-diffusion malaria model accounting for asymptomatic carriers.
- Author
-
Shi, Yangyang, Chen, Fangyuan, Wang, Liping, and Zhang, Xuebing
- Subjects
BASIC reproduction number ,GLOBAL asymptotic stability ,MALARIA ,BEHAVIORAL assessment ,MALARIA prevention - Abstract
A significant proportion of malaria infections in humans exhibit no symptoms, but it is a reservoir for maintaining malaria transmission. A time periodic reaction-diffusion model for malaria spread is introduced in this paper, incorporating spatial heterogeneity, incubation periods, symptomatic and asymptomatic carriers. This paper introduces the concept of the basic reproduction number R 0 , which is defined as the spectral radius of the next generation operator, and we present some preliminary results by elementary analysis. The threshold dynamic behavior analysis shows that when R 0 < 1 , the disease is extinct, and when R 0 > 1 , the disease is persistent. We investigate the case of constant system parameters, focusing on the global asymptotic stability of the disease-free steady state when R 0 = 1 . In the numerical simulation section, we validate the theoretical results obtained, and then use elasticity analysis methods to explore the influence of parameters on the output solution. In addition, sensitivity analysis of the basic reproduction number under homogeneous conditions indicates direction of controlling malaria transmission. And several control measures are evaluated in the following steps. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
13. Modeling the impact of non-human host predation on the transmission of Chagas disease.
- Author
-
Dai X, Wu X, Jiang J, and Rong L
- Subjects
- Animals, Humans, Models, Biological, Insect Vectors parasitology, Triatominae parasitology, Mathematical Concepts, Trypanosoma cruzi, Chagas Disease transmission, Predatory Behavior, Basic Reproduction Number statistics & numerical data
- Abstract
In addition to the traditional transmission route via the biting-and-defecating process, non-human host predation of triatomines is recognized as another significant avenue for Chagas disease transmission. In this paper, we develop an eco-epidemiological model to investigate the impact of predation on the disease's spread. Two critical thresholds, R
v (the basic reproduction number of triatomines) and Rp (the basic reproduction number of the Chagas parasite), are derived to delineate the model's dynamics. Through the construction of appropriate Lyapunov functions and the application of the Bendixson-Dulac theorem, the global asymptotic stabilities of the equilibria are fully established. The vector-free equilibrium E0 p (the basic reproduction number of the Chagas parasite), are derived to delineate the model's dynamics. Through the construction of appropriate Lyapunov functions and the application of the Bendixson-Dulac theorem, the global asymptotic stabilities of the equilibria are fully established. The vector-free equilibrium E0 is globally stable when Rv p <1. E1 , the disease-free equilibrium, is globally stable when Rv p >1 and R0 p <1, while the endemic equilibrium E∗ is globally stable when both Rv p >1 and R0 p >1. Numerical simulations highlight that the degree of host predation on triatomines, influenced by non-human hosts activities, can variably increase or decrease the Chagas disease transmission risk. Specifically, low or high levels of host predation can reduce R0 p to below unity, while intermediate levels may increase the infected host populations, albeit with a reduction in R0 p . These findings highlight the role played by non-human hosts and offer crucial insights for the prevention and control of Chagas disease., Competing Interests: Declaration of competing interest The article is original and the authors declare that they have no competing of interests., (Copyright © 2024 Elsevier Inc. All rights reserved.)- Published
- 2024
- Full Text
- View/download PDF
14. Global stability and optimal control of an age-structured SVEIR epidemic model with waning immunity and relapses.
- Author
-
Ma S, Tian T, and Huo H
- Subjects
- Humans, China epidemiology, Mathematical Concepts, Models, Biological, Age Factors, Epidemiological Models, Nonlinear Dynamics, Incidence, Prevalence, Basic Reproduction Number statistics & numerical data, Epidemics statistics & numerical data, Epidemics prevention & control, Recurrence, Tuberculosis epidemiology, Tuberculosis prevention & control, Tuberculosis immunology
- Abstract
The efficacy of vaccination, incomplete treatment and disease relapse are critical challenges that must be faced to prevent and control the spread of infectious diseases. Age heterogeneity is also a crucial factor for this study. In this paper, we investigate a new age-structured SVEIR epidemic model with the nonlinear incidence rate, waning immunity, incomplete treatment and relapse. Next, the asymptotic smoothness, the uniform persistence and the existence of interior global attractor of the solution semi-flow generated by the system are given. We define the basic reproduction number R 0 and prove the existence of the equilibria of the model. And we study the global asymptotic stability of the equilibria. Then the parameters of the model are estimated using tuberculosis data in China. The sensitivity analysis of R 0 is derived by the Partial Rank Correlation Coefficient method. These main theoretical results are applied to analyze and predict the trend of tuberculosis prevalence in China. Finally, the optimal control problem of the model is discussed. We choose to take strengthening treatment and controlling relapse as the control parameters. The necessary condition for optimal control is established., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)
- Published
- 2024
- Full Text
- View/download PDF
15. Prevention and control of Ebola virus transmission: mathematical modelling and data fitting.
- Author
-
Ren H and Xu R
- Subjects
- Humans, Animals, Sierra Leone epidemiology, Epidemics statistics & numerical data, Epidemics prevention & control, Computer Simulation, Epidemiological Models, Disease Outbreaks prevention & control, Disease Outbreaks statistics & numerical data, Hemorrhagic Fever, Ebola transmission, Hemorrhagic Fever, Ebola prevention & control, Hemorrhagic Fever, Ebola epidemiology, Basic Reproduction Number statistics & numerical data, Mathematical Concepts, Models, Biological, Ebolavirus pathogenicity, Ebolavirus physiology
- Abstract
The Ebola virus disease (EVD) has been endemic since 1976, and the case fatality rate is extremely high. EVD is spread by infected animals, symptomatic individuals, dead bodies, and contaminated environment. In this paper, we formulate an EVD model with four transmission modes and a time delay describing the incubation period. Through dynamical analysis, we verify the importance of blocking the infection source of infected animals. We get the basic reproduction number without considering the infection source of infected animals. And, it is proven that the model has a globally attractive disease-free equilibrium when the basic reproduction number is less than unity; the disease eventually becomes endemic when the basic reproduction number is greater than unity. Taking the EVD epidemic in Sierra Leone in 2014-2016 as an example, we complete the data fitting by combining the effect of the media to obtain the unknown parameters, the basic reproduction number and its time-varying reproduction number. It is shown by parameter sensitivity analysis that the contact rate and the removal rate of infected group have the greatest influence on the prevalence of the disease. And, the disease-controlling thresholds of these two parameters are obtained. In addition, according to the existing vaccination strategy, only the inoculation ratio in high-risk areas is greater than 0.4, the effective reproduction number can be less than unity. And, the earlier the vaccination time, the greater the inoculation ratio, and the faster the disease can be controlled., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)
- Published
- 2024
- Full Text
- View/download PDF
16. A mathematical model of COVID-19 with multiple variants of the virus under optimal control in Ghana.
- Author
-
Kim YR, Min Y, and Okogun-Odompley JN
- Subjects
- Humans, Ghana epidemiology, COVID-19 prevention & control, COVID-19 epidemiology, COVID-19 virology, COVID-19 transmission, SARS-CoV-2 genetics, Basic Reproduction Number, Models, Theoretical
- Abstract
In this paper, we suggest a mathematical model of COVID-19 with multiple variants of the virus under optimal control. Mathematical modeling has been used to gain deeper insights into the transmission of COVID-19, and various prevention and control strategies have been implemented to mitigate its spread. Our model is a SEIR-based model for multi-strains of COVID-19 with 7 compartments. We also consider the circulatory structure to account for the termination of immunity for COVID-19. The model is established in terms of the positivity and boundedness of the solution and the existence of equilibrium points, and the local stability of the solution. As a result of fitting data of COVID-19 in Ghana to the model, the basic reproduction number of the original virus and Delta variant was estimated to be 1.9396, and the basic reproduction number of the Omicron variant was estimated to be 3.4905, which is 1.8 times larger than that. We observe that even small differences in the incubation and recovery periods of two strains with the same initial transmission rate resulted in large differences in the number of infected individuals. In the case of COVID-19, infections caused by the Omicron variant occur 1.5 to 10 times more than those caused by the original virus. In terms of the optimal control strategy, we formulate three control strategies focusing on social distancing, vaccination, and testing-treatment. We have developed an optimal control model for the three strategies outlined above for the multi-strain model using the Pontryagin's Maximum Principle. Through numerical simulations, we analyze three optimal control strategies for each strain and also consider combinations of the two control strategies. As a result of the simulation, all control strategies are effective in reducing disease spread, in particular, vaccination strategies are more effective than the other two control strategies. In addition the combination of the two strategies also reduces the number of infected individuals by 1/10 compared to implementing one strategy, even when mild levels are implemented. Finally, we show that if the testing-treatment strategy is not properly implemented, the number of asymptomatic and unidentified infections may surge. These results could help guide the level of government intervention and prevention strategy formulation., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Kim et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)
- Published
- 2024
- Full Text
- View/download PDF
17. A stochastic SEIHR model for COVID-19 data fluctuations
- Author
-
Ruiwu Niu, Michael Antonie van Wyk, Yin-Chi Chan, Eric Wong, and Guanrong Chen
- Subjects
Original Paper ,2019-20 coronavirus outbreak ,Stochastic stability ,Stochastic differential equation ,Coronavirus disease 2019 (COVID-19) ,Computer science ,Applied Mathematics ,Mechanical Engineering ,Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ,COVID-19 ,Aerospace Engineering ,Ocean Engineering ,SEIHR model ,Control and Systems Engineering ,Applied mathematics ,Electrical and Electronic Engineering ,Noise level ,Data fluctuation ,Basic reproduction number - Abstract
Although deterministic compartmental models are useful for predicting the general trend of a disease's spread, they are unable to describe the random daily fluctuations in the number of new infections and hospitalizations, which is crucial in determining the necessary healthcare capacity for a specified level of risk. In this paper, we propose a stochastic SEIHR (sSEIHR) model to describe such random fluctuations and provide sufficient conditions for stochastic stability of the disease-free equilibrium, based on the basic reproduction number that we estimated. Our extensive numerical results demonstrate strong threshold behavior near the estimated basic reproduction number, suggesting that the necessary conditions for stochastic stability are close to the sufficient conditions derived. Furthermore, we found that increasing the noise level slightly reduces the final proportion of infected individuals. In addition, we analyze COVID-19 data from various regions worldwide and demonstrate that by changing only a few parameter values, our sSEIHR model can accurately describe both the general trend and the random fluctuations in the number of daily new cases in each region, allowing governments and hospitals to make more accurate caseload predictions using fewer compartments and parameters than other comparable stochastic compartmental models.
- Published
- 2021
18. Complex dynamics of an epidemic model with saturated media coverage and recovery
- Author
-
Yanni Xiao and Tangjuan Li
- Subjects
Original Paper ,Computer science ,Applied Mathematics ,Mechanical Engineering ,Nonlinear recovery function ,Aerospace Engineering ,Media coverage ,Ocean Engineering ,computer.software_genre ,Basic reproduction number ,Complex dynamics ,Mathematical model ,Saddle-node bifurcation ,Media impact ,Control and Systems Engineering ,Data mining ,Hopf bifurcation ,Electrical and Electronic Engineering ,Epidemic model ,computer - Abstract
During the outbreak of emerging infectious diseases, media coverage and medical resource play important roles in affecting the disease transmission. To investigate the effects of the saturation of media coverage and limited medical resources, we proposed a mathematical model with extra compartment of media coverage and two nonlinear functions. We theoretically and numerically investigate the dynamics of the proposed model. Given great difficulties caused by high nonlinearity in theoretical analysis, we separately considered subsystems with only nonlinear recovery or with only saturated media impact. For the model with only nonlinear recovery, we theoretically showed that backward bifurcation can occur and multiple equilibria may coexist under certain conditions in this case. Numerical simulations reveal the rich dynamic behaviors, including forward-backward bifurcation, Hopf bifurcation, saddle-node bifurcation, homoclinic bifurcation and unstable limit cycle. So the limitation of medical resources induces rich dynamics and causes much difficulties in eliminating the infectious diseases. We then investigated the dynamics of the system with only saturated media impact and concluded that saturated media impact hardly induces the complicated dynamics. Further, we parameterized the proposed model on the basis of the COVID-19 case data in mainland China and data related to news items, and estimated the basic reproduction number to be 2.86. Sensitivity analyses were carried out to quantify the relative importance of parameters in determining the cumulative number of infected individuals at the end of the first month of the outbreak. Combining with numerical analyses, we suggested that providing adequate medical resources and improving media response to infection or individuals' response to mass media may reduce the cumulative number of the infected individuals, which mitigates the transmission dynamics during the early stage of the COVID-19 pandemic.
- Published
- 2022
19. Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic
- Author
-
Omar Khyar and Karam Allali
- Subjects
General incidence function ,Generalization ,Global stability analysis ,Aerospace Engineering ,Ocean Engineering ,01 natural sciences ,Stability (probability) ,0103 physical sciences ,Quantitative Biology::Populations and Evolution ,Applied mathematics ,Electrical and Electronic Engineering ,010301 acoustics ,Mathematics ,Equilibrium point ,Original Paper ,Strain (chemistry) ,Applied Mathematics ,Mechanical Engineering ,Dynamics (mechanics) ,Order (ring theory) ,COVID-19 ,Multi-strain epidemic model ,Basic reproduction number ,Control and Systems Engineering ,Epidemic model ,SEIR - Abstract
This paper investigates the global stability analysis of two-strain epidemic model with two general incidence rates. The problem is modelled by a system of six nonlinear ordinary differential equations describing the evolution of susceptible, exposed, infected and removed individuals. The wellposedness of the suggested model is established in terms of existence, positivity and boundedness of solutions. Four equilibrium points are given, namely the disease-free equilibrium, the endemic equilibrium with respect to strain 1, the endemic equilibrium with respect to strain 2, and the last endemic equilibrium with respect to both strains. By constructing suitable Lyapunov functional, the global stability of the disease-free equilibrium is proved depending on the basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0. Furthermore, using other appropriate Lyapunov functionals, the global stability results of the endemic equilibria are established depending on the strain 1 reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^{1}_0$$\end{document}R01 and the strain 2 reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^{2}_0$$\end{document}R02. Numerical simulations are performed in order to confirm the different theoretical results. It was observed that the model with a generalized incidence functions encompasses a large number of models with classical incidence functions and it gives a significant wide view about the equilibria stability. Numerical comparison between the model results and COVID-19 clinical data was conducted. Good fit of the model to the real clinical data was remarked. The impact of the quarantine strategy on controlling the infection spread is discussed. The generalization of the problem to a more complex compartmental model is illustrated at the end of this paper.
- Published
- 2020
20. Vaccination control of an epidemic model with time delay and its application to COVID-19
- Author
-
Xin Wang, Guoqiang Luo, Junli Tao, Shidong Zhai, Tao Huang, and Ping Zhou
- Subjects
Original Paper ,State delayed feedback ,Coronavirus disease 2019 (COVID-19) ,Applied Mathematics ,Mechanical Engineering ,Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ,Vaccination ,Linear system ,Control (management) ,Stability (learning theory) ,Aerospace Engineering ,Ocean Engineering ,01 natural sciences ,Control and Systems Engineering ,Control theory ,Epidemic model ,0103 physical sciences ,Electrical and Electronic Engineering ,010301 acoustics ,Basic reproduction number ,Time delay ,Mathematics - Abstract
This paper studies an SEIR-type epidemic model with time delay and vaccination control. The vaccination control is applied when the basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0>1$$\end{document}R0>1. The vaccination strategy is expressed as a state delayed feedback which is related to the current and previous state of the epidemic model, and makes the model become a linear system in new coordinates. For the presence and absence of vaccination control, we investigate the nonnegativity and boundedness of the model, respectively. We obtain some sufficient conditions for the eigenvalues of the linear system such that the nonnegativity of the epidemic model can be guaranteed when the vaccination strategy is applied. In addition, we study the stability of disease-free equilibrium when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_01$$\end{document}R0>1. Finally, we use the obtained theoretical results to simulate the vaccination strategy to control the spread of COVID-19.
- Published
- 2021
21. Exploring the influence of burial and cremation practices on Nipah virus transmission: a SIRD model analysis
- Author
-
Kubra, Khadija Tul, Gulshan, Samra, and Ali, Rooh
- Published
- 2024
- Full Text
- View/download PDF
22. Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III
- Author
-
Chhetri, Bishal, Vamsi, D. K. K., and Sanjeevi, Carani B
- Published
- 2024
- Full Text
- View/download PDF
23. Quantitative analysis of a fractional order of the $ SEI_{c}\, I_{\eta} VR $ epidemic model with vaccination strategy.
- Author
-
Alshareef, Abeer
- Subjects
BASIC reproduction number ,EPIDEMIOLOGICAL models ,VACCINATION ,COMMUNICABLE diseases ,QUANTITATIVE research ,EPIDEMICS - Abstract
This work focused on studying the effect of vaccination rate κ on reducing the outbreak of infectious diseases, especially if the infected individuals do not have any symptoms. We employed the fractional order derivative in this study since it has a high degree of accuracy. Recently, a lot of scientists have been interested in fractional-order models. It is considered a modern direction in the mathematical modeling of epidemiology systems. Therefore, a fractional order of the SEIR epidemic model with two types of infected groups and vaccination strategy was formulated and investigated in this paper. The proposed model includes the following classes: susceptible S (t) , exposed E (t) , asymptomatic infected I c (t) , symptomatic infected I η (t) , vaccinated V (t) , and recovered R (t) . We began our study by creating the existence, non-negativity, and boundedness of the solutions of the proposed model. Moreover, we established the basic reproduction number R 0 , that was used to examine the existence and stability of the equilibrium points for the presented model. By creating appropriate Lyapunov functions, we proved the global stability of the free-disease equilibrium point and endemic equilibrium point. We concluded that the free-disease equilibrium point is globally asymptotically stable (GAS) when R 0 ≤ 1 , while the endemic equilibrium point is GAS if R 0 > 1 . Therefore, we indicated the increasing vaccination rate κ leads to reducing R 0 . These findings confirm the important role of vaccination rate κ in fighting the spread of infectious diseases. Moreover, the numerical simulations were introduced to validate theoretical results that are given in this work by applying the predictor-corrector PECE method of Adams-Bashforth-Moulton. Further more, the impact of the vaccination rate κ was explored numerically and we found that, as κ increases, the R 0 is decreased. This means the vaccine can be useful in reducing the spread of infectious diseases. This work focused on studying the effect of vaccination rate on reducing the outbreak of infectious diseases, especially if the infected individuals do not have any symptoms. We employed the fractional order derivative in this study since it has a high degree of accuracy. Recently, a lot of scientists have been interested in fractional-order models. It is considered a modern direction in the mathematical modeling of epidemiology systems. Therefore, a fractional order of the SEIR epidemic model with two types of infected groups and vaccination strategy was formulated and investigated in this paper. The proposed model includes the following classes: susceptible , exposed , asymptomatic infected , symptomatic infected , vaccinated , and recovered . We began our study by creating the existence, non-negativity, and boundedness of the solutions of the proposed model. Moreover, we established the basic reproduction number , that was used to examine the existence and stability of the equilibrium points for the presented model. By creating appropriate Lyapunov functions, we proved the global stability of the free-disease equilibrium point and endemic equilibrium point. We concluded that the free-disease equilibrium point is globally asymptotically stable (GAS) when , while the endemic equilibrium point is GAS if . Therefore, we indicated the increasing vaccination rate leads to reducing . These findings confirm the important role of vaccination rate in fighting the spread of infectious diseases. Moreover, the numerical simulations were introduced to validate theoretical results that are given in this work by applying the predictor-corrector PECE method of Adams-Bashforth-Moulton. Further more, the impact of the vaccination rate was explored numerically and we found that, as increases, the is decreased. This means the vaccine can be useful in reducing the spread of infectious diseases. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Dynamics in a delayed rumor propagation model with logistic growth and saturation incidence.
- Author
-
Rongrong Yin and Muhammadhaji, Ahmadjan
- Subjects
BASIC reproduction number ,GLOBAL asymptotic stability ,RUMOR ,INFECTIOUS disease transmission - Abstract
This paper studies a delayed rumor propagation model with logistic growth and saturation incidence. The next generation matrix method, some inequality techniques, the Lyapunov-LaSalle invariance principle, and the Lyapunov method are used in this paper. Our results indicate that if the basic regeneration number (which is analogous to the basic reproduction number in disease transmission models) is less than 1, the rumor-free equilibrium point (which is analogous to the disease-free equilibrium point in disease transmission models) is globally stable. If the basic regeneration number is greater than 1, then the rumor is permanent, and some sufficient conditions are obtained for local and global asymptotic stability of the rumor prevailing equilibrium point (which is analogous to the endemic equilibrium point in disease transmission models). Finally, three examples with numerical simulations are presented to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. Modeling and analysis of Cystic Echinococcosis epidemic model with health education.
- Author
-
Qianqian Cui, Qiang Zhang, and Zengyun Hu
- Subjects
HEALTH education ,HYGIENE ,BASIC reproduction number ,ECHINOCOCCOSIS ,ANIMAL health ,PUBLIC health - Abstract
The prevention and control of the spread of Cystic Echinococcosis is an important public health issue. Health education has been supported by many governments because it can increase public awareness of echinococcosis, promote the development of personal hygiene habits, and subsequently reduce the transmission of echinococcosis. In this paper, a dynamic model of echinococcosis is used to integrate all aspects of health education. Theoretical analysis and numerical model fitting were used to quantitatively analysed by the impact of health education on the spread of echinococcosis. Theoretical findings indicate that the basic reproduction number is crucial in determining the prevalence of echinococcosis within a given geographical area. The parameters of the model were estimated and fitted by using data from the Ningxia Hui Autonomous Region in China, and the sensitivity of the basic reproduction number was analysed by using the partial rank correlation coefficient method. These findings illustrate that all aspects of health education demonstrate a negative correlation with the basic reproduction number, suggesting the effectiveness of health education in reducing the basic reproduction number and mitigating the transmission of echinococcosis, which is consistent with reality. Particularly, the basic reproduction number showed a strong negative correlation with the burial rate of infected livestock (b) and the incidence of infected livestock viscera that is not fed to dogs (q). This paper further analyzes the implementation plan for canine deworming rates and sheep immunity rates, as well as the transmission of infected hosts over time under different parameters b and q. According to the findings, emphasizing the management of infected livestock in health education has the potential to significantly reduce the risk of echinococcosis transmission. This study will provide scientific support for the creation of higher quality health education initiatives. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
26. Analyzing the Asymptotic Behavior of an Extended SEIR Model with Vaccination for COVID-19.
- Author
-
Papageorgiou, Vasileios E., Vasiliadis, Georgios, and Tsaklidis, George
- Subjects
GLOBAL analysis (Mathematics) ,COVID-19 vaccines ,BASIC reproduction number ,KALMAN filtering ,COVID-19 pandemic ,DIFFERENTIAL equations - Abstract
Several research papers have attempted to describe the dynamics of COVID-19 based on systems of differential equations. These systems have taken into account quarantined or isolated cases, vaccinations, control measures, and demographic parameters, presenting propositions regarding theoretical results that often investigate the asymptotic behavior of the system. In this paper, we discuss issues that concern the theoretical results proposed in the paper "An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter". We propose detailed explanations regarding the resolution of these issues. Additionally, this paper focuses on extending the local stability analysis of the disease-free equilibrium, as presented in the aforementioned paper, while emphasizing the derivation of theorems that validate the global stability of both epidemic equilibria. Emphasis is placed on the basic reproduction number R 0 , which determines the asymptotic behavior of the system. This index represents the expected number of secondary infections that are generated from an already infected case in a population where almost all individuals are susceptible. The derived propositions can inform health authorities about the long-term behavior of the phenomenon, potentially leading to more precise and efficient public measures. Finally, it is worth noting that the examined paper still presents an interesting epidemiological scheme, and the utilization of the Kalman filtering approach remains one of the state-of-the-art methods for modeling epidemic phenomena. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. A discrete SIS-model built on the strictly positive scheme.
- Author
-
Choiński, Marcin
- Subjects
BASIC reproduction number ,DISCRETIZATION methods - Abstract
In this paper we introduce and analyze a discrete SIS epidemic model for a homogeneous population. As a discretization method the strictly positive scheme was chosen. The presented model is built from its continuous counterpart known from literature. We firstly present basic properties of the system. Later we discuss local stability of stationary states and global stability for the disease-free stationary state. The results for this state are expressed with the use of the basic reproduction number. The main conclusion from our work is that conditions for stability of the stationary states do not depend on the step size of the discretization method. This fact stays in contrary to other discrete models analyzed in our previous papers. Theoretical results are accomplished with numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
28. ON THE STABILITY ANALYSIS OF A FRACTIONAL ORDER EPIDEMIC MODEL INCLUDING THE GENERAL FORMS OF NONLINEAR INCIDENCE AND TREATMENT FUNCTION.
- Author
-
KARAOĞLU, Esra
- Subjects
BASIC reproduction number ,NONLINEAR functions ,EPIDEMICS ,COMPUTER simulation - Abstract
In this paper, we propose to study a SEIR model of fractional order with an incidence and a treatment function. The incidence and treatment functions included in the model are general nonlinear functions that satisfy some meaningful biological hypotheses. Under these hypotheses, it is shown that the disease free equilibrium point of the proposed model is locally and globally asymptotically stable when the reproduction number R
0 is smaller than 1. When R0 > 1, it is established that the endemic equilibrium of the studied system is uniformly asymptotically stable. Finally, some numerical simulations are provided to illustrate the theory. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
29. The spatiotemporal transmission dynamics of COVID-19 among multiple regions: a modeling study in Chinese provinces
- Author
-
Fei Tian, Hualiang Lin, Jiali Li, Qiaojuan Jia, and Guanghu Zhu
- Subjects
Spatiotemporal transmission ,Original Paper ,Human mobility ,Coronavirus disease 2019 (COVID-19) ,Reproduction number ,Applied Mathematics ,Mechanical Engineering ,Aerospace Engineering ,Outbreak ,COVID-19 ,Ocean Engineering ,Disease control ,law.invention ,Prevention and control ,Geography ,Transmission (mechanics) ,Ordinary differential system ,Control and Systems Engineering ,law ,Economic geography ,Electrical and Electronic Engineering ,China ,Spatial diffusion ,Basic reproduction number - Abstract
Current explosive outbreak of COVID-19 around the world is a complex spatiotemporal process with hidden interactions between viruses and humans. This study aims at clarifying the transmission patterns and the driving mechanism that contributed to the COVID-19 prevalence across the provinces of China. Thus, a new dynamical transmission model is established by an ordinary differential system. The model takes into account the hidden circulation of COVID-19 virus among/within humans, which incorporates the spatial diffusion of infection by parameterizing human mobility. Theoretical analysis indicates that the basic reproduction number is a unique epidemic threshold, which can unite infectivity in each region by human mobility and can totally determine whether COVID-19 proceeds among multiple regions. By validating the model with real epidemic data in China, it is found that (1) if without any intervention, COVID-19 would overrun China within three months, resulting in more than 1.1 billion clinical infections and 0.2 billion subclinical infections; (2) high frequency of human mobility can trigger COVID-19 diffusion across each province in China, no matter where the initial infection locates; (3) travel restrictions and other non-pharmaceutical interventions must be implemented simultaneously for disease control; and (4) infection sites in central and east (rather than west and northeast) of China would easily stimulate quick diffusion of COVID-19 in the whole country. Supplementary Information The online version supplementary material available at 10.1007/s11071-021-07001-1.
- Published
- 2021
30. A hybrid Lagrangian-Eulerian model for vector-borne diseases.
- Author
-
Gao D and Yuan X
- Subjects
- Humans, Animals, Disease Vectors, Epidemiological Models, Basic Reproduction Number statistics & numerical data, Vector Borne Diseases transmission, Vector Borne Diseases epidemiology, Vector Borne Diseases prevention & control, Mathematical Concepts, Models, Biological, Computer Simulation
- Abstract
In this paper, a multi-patch and multi-group vector-borne disease model is proposed to study the effects of host commuting (Lagrangian approach) and/or vector migration (Eulerian approach) on disease spread. We first define the basic reproduction number of the model, R 0 , which completely determines the global dynamics of the model system. Namely, if R 0 ≤ 1 , then the disease-free equilibrium is globally asymptotically stable, and if R 0 > 1 , then there exists a unique endemic equilibrium which is globally asymptotically stable. Then, we show that the basic reproduction number has lower and upper bounds which are independent of the host residence times matrix and the vector migration matrix. In particular, nonhomogeneous mixing of hosts and vectors in a homogeneous environment generally increases disease persistence and the basic reproduction number of the model attains its minimum when the distributions of hosts and vectors are proportional. Moreover, R 0 can also be estimated by the basic reproduction numbers of disconnected patches if the environment is homogeneous. The optimal vector control strategy is obtained for a special scenario. In the two-patch and two-group case, we numerically analyze the dependence of the basic reproduction number and the total number of infected people on the host residence times matrix and illustrate the optimal vector control strategy in homogeneous and heterogeneous environments., (© 2024. The Author(s).)
- Published
- 2024
- Full Text
- View/download PDF
31. A simulation-based approach for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data.
- Author
-
Ogi-Gittins I, Hart WS, Song J, Nash RK, Polonsky J, Cori A, Hill EM, and Thompson RN
- Subjects
- Humans, Incidence, Time Factors, Computer Simulation, Wales epidemiology, Epidemiological Models, Bayes Theorem, Influenza, Human epidemiology, Influenza, Human transmission, Disease Outbreaks statistics & numerical data, Basic Reproduction Number statistics & numerical data
- Abstract
Tracking pathogen transmissibility during infectious disease outbreaks is essential for assessing the effectiveness of public health measures and planning future control strategies. A key measure of transmissibility is the time-dependent reproduction number, which has been estimated in real-time during outbreaks of a range of pathogens from disease incidence time series data. While commonly used approaches for estimating the time-dependent reproduction number can be reliable when disease incidence is recorded frequently, such incidence data are often aggregated temporally (for example, numbers of cases may be reported weekly rather than daily). As we show, commonly used methods for estimating transmissibility can be unreliable when the timescale of transmission is shorter than the timescale of data recording. To address this, here we develop a simulation-based approach involving Approximate Bayesian Computation for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data. We first use a simulated dataset representative of a situation in which daily disease incidence data are unavailable and only weekly summary values are reported, demonstrating that our method provides accurate estimates of the time-dependent reproduction number under such circumstances. We then apply our method to two outbreak datasets consisting of weekly influenza case numbers in 2019-20 and 2022-23 in Wales (in the United Kingdom). Our simple-to-use approach will allow accurate estimates of time-dependent reproduction numbers to be obtained from temporally aggregated data during future infectious disease outbreaks., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier B.V. All rights reserved.)
- Published
- 2024
- Full Text
- View/download PDF
32. Modelling the impact of precaution on disease dynamics and its evolution.
- Author
-
Cheng T and Zou X
- Subjects
- Humans, Disease Susceptibility epidemiology, Epidemiological Models, Biological Evolution, Computer Simulation, Basic Reproduction Number statistics & numerical data, Mathematical Concepts, Epidemics statistics & numerical data, Epidemics prevention & control, Communicable Diseases epidemiology, Communicable Diseases transmission, Models, Biological
- Abstract
In this paper, we introduce the notion of practically susceptible population, which is a fraction of the biologically susceptible population. Assuming that the fraction depends on the severity of the epidemic and the public's level of precaution (as a response of the public to the epidemic), we propose a general framework model with the response level evolving with the epidemic. We firstly verify the well-posedness and confirm the disease's eventual vanishing for the framework model under the assumption that the basic reproduction number R 0 < 1 . For R 0 > 1 , we study how the behavioural response evolves with epidemics and how such an evolution impacts the disease dynamics. More specifically, when the precaution level is taken to be the instantaneous best response function in literature, we show that the endemic dynamic is convergence to the endemic equilibrium; while when the precaution level is the delayed best response, the endemic dynamic can be either convergence to the endemic equilibrium, or convergence to a positive periodic solution. Our derivation offers a justification/explanation for the best response used in some literature. By replacing "adopting the best response" with "adapting toward the best response", we also explore the adaptive long-term dynamics., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)
- Published
- 2024
- Full Text
- View/download PDF
33. Threshold dynamics of a reaction-advection-diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity.
- Author
-
Wu P, Salmaniw Y, and Wang X
- Subjects
- Humans, Animals, Epidemiological Models, Computer Simulation, Water Movements, Seasons, Basic Reproduction Number statistics & numerical data, Schistosomiasis transmission, Schistosomiasis epidemiology, Mathematical Concepts, Epidemics statistics & numerical data, Models, Biological
- Abstract
Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction-advection-diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number R 0 and show that the disease-free periodic solution is globally attractive when R 0 < 1 whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case when R 0 > 1 . Moreover, we find that R 0 is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows., (© 2024. The Author(s).)
- Published
- 2024
- Full Text
- View/download PDF
34. Transmission dynamics of a reaction-advection-diffusion dengue fever model with seasonal developmental durations and intrinsic incubation periods.
- Author
-
Zha Y and Jiang W
- Subjects
- Animals, Humans, China epidemiology, Aedes virology, Aedes growth & development, Epidemiological Models, Dengue Virus growth & development, Computer Simulation, Seasons, Dengue transmission, Basic Reproduction Number statistics & numerical data, Models, Biological, Mosquito Vectors growth & development, Mosquito Vectors virology, Mathematical Concepts, Infectious Disease Incubation Period
- Abstract
In this paper, we propose a reaction-advection-diffusion dengue fever model with seasonal developmental durations and intrinsic incubation periods. Firstly, we establish the well-posedness of the model. Secondly, we define the basic reproduction number ℜ 0 for this model and show that ℜ 0 is a threshold parameter: if ℜ 0 < 1 , then the disease-free periodic solution is globally attractive; if ℜ 0 > 1 , the system is uniformly persistent. Thirdly, we study the global attractivity of the positive steady state when the spatial environment is homogeneous and the advection of mosquitoes is ignored. As an example, we use the model to investigate the dengue fever transmission case in Guangdong Province, China, and explore the impact of model parameters on ℜ 0 . Our findings indicate that ignoring seasonality may underestimate ℜ 0 . Additionally, the spatial heterogeneity of transmission may increase the risk of disease transmission, while the increase of seasonal developmental durations, intrinsic incubation periods and advection rates can all reduce the risk of disease transmission., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)
- Published
- 2024
- Full Text
- View/download PDF
35. A novel within-host model of HIV and nutrition.
- Author
-
Timsina AN, Liyanage YR, Martcheva M, and Tuncer N
- Subjects
- Humans, CD4 Lymphocyte Count, Nutritional Status, Models, Biological, Algorithms, HIV-1, HIV Infections, Monte Carlo Method, Viral Load, Computer Simulation, Basic Reproduction Number statistics & numerical data
- Abstract
In this paper we develop a four compartment within-host model of nutrition and HIV. We show that the model has two equilibria: an infection-free equilibrium and infection equilibrium. The infection free equilibrium is locally asymptotically stable when the basic reproduction number $ \mathcal{R}_0 < 1 $, and unstable when $ \mathcal{R}_0 > 1 $. The infection equilibrium is locally asymptotically stable if $ \mathcal{R}_0 > 1 $ and an additional condition holds. We show that the within-host model of HIV and nutrition is structured to reveal its parameters from the observations of viral load, CD4 cell count and total protein data. We then estimate the model parameters for these 3 data sets. We have also studied the practical identifiability of the model parameters by performing Monte Carlo simulations, and found that the rate of clearance of the virus by immunoglobulins is practically unidentifiable, and that the rest of the model parameters are only weakly identifiable given the experimental data. Furthermore, we have studied how the data frequency impacts the practical identifiability of model parameters.
- Published
- 2024
- Full Text
- View/download PDF
36. Analysis on a spatial SIS epidemic model with saturated incidence function in advective environments: II. Varying total population.
- Author
-
Chen, Xiaodan and Cui, Renhao
- Subjects
- *
BASIC reproduction number , *INFECTIOUS disease transmission , *EPIDEMICS , *COMMUNICABLE diseases - Abstract
This paper is concerned with a reaction-diffusion SIS (susceptible-infected-susceptible) epidemic model governed by a saturated incidence function and linear birth-death growth in advective environments. The related model without birth and death case has been studied in our previous work [8]. In this paper, our main purpose is to investigate the combined effects of varying total population, saturation infection mechanism and spatial heterogeneity on the transmission dynamics and spatial distribution of disease. The extinction and persistence of the infectious disease in terms of the basic reproduction number are established. We discuss the global attractivity of the equilibria in two special cases and explore the asymptotic profiles of the endemic equilibrium with respect to the dispersal and advection rates. Compared with the results for the model without birth and death in [8] , our findings indicate that the linear birth-death growth can enhance the persistence of an infectious disease and may provide some prospective applications in disease prevention and control. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
37. Analysis of a delayed spatiotemporal model of HBV infection with logistic growth.
- Author
-
Foko, Séverin and Tadmon, Calvin
- Subjects
HEPATITIS B ,VIRUS diseases ,ENDEMIC diseases ,HEPATITIS B virus ,HOPF bifurcations ,BASIC reproduction number - Abstract
In this paper, following previous works of ours, we deal with a mathematical model of hepatitis B virus (HBV) infection. We assume spatial diffusion of free HBV particles, logistic growth for both healthy and infected hepatocytes, and use the standard incidence function for viral infection. Moreover, one time delay is introduced to account for actual virus production. Another time delay is used to account for virus maturation. The existence, uniqueness, positivity and boundedness of solutions are established. Analyzing the model qualitatively and using a Lyapunov functional, we establish the existence of a threshold $ \mathcal {T}_0 $ T 0 such that, if the basic reproduction number $ \mathcal {R}_0 $ R 0 verifies $ \mathcal {R}_0\leq \mathcal {T}_0{ \lt }1 $ R 0 ≤ T 0 < 1 , the infection-free equilibrium is globally asymptotically stable. When $ \mathcal {R}_0 $ R 0 is greater than one, we discuss the local asymptotic stability of the unique endemic equilibrium and the occurrence of a Hopf bifurcation. Also, when $ \mathcal {R}_0 $ R 0 is greater than one, the system is uniformly persistent, which means that the HBV infection is endemic. Finally, we carry out some relevant numerical simulations to clarify and interpret the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
38. A continuous time Markov chain model for the dynamics of bovine tuberculosis in humans and cattle.
- Author
-
Stephano, Mussa A., Irunde, Jacob I., Mwasunda, Joshua A., and Chacha, Chacha S.
- Abstract
Bovine tuberculosis (bTB) is a disease of major public health concern and economic importance. The disease affects the livelihood of rural livestock farmers, economies of developing countries, human and animal health. In this paper, both deterministic and continuous time Markov chain (CTMC) models are formulated and analyzed to study the dynamics of bovine tuberculosis in humans and cattle. The next generation matrix method is applied to compute the basic reproduction number R 0 for the deterministic model while the multitype branching process is applied to compute the stochastic threshold for CTMC model. The normalized forward sensitivity index method is used to compute sensitivity indices of model parameters with respect to basic reproduction number R 0 . The results reveal that infection rate among cattle is the most positive sensitive parameter whereas cattle's natural death is the most negative sensitive parameter. This suggests that more efforts should be directed at reducing number of infected cattle for possible control of the spread of bTB in human and cattle populations. Numerical simulations for the CTMC stochastic model using 10,000 sample paths is carried out to compute probabilities for disease extinction by varying initial values for infected classes. The results show that, the solutions of CTMC stochastic model are relatively close to the deterministic model solutions. The possibility of bTB extinction is high when it emanates from either humans or infectious dairy products or from a small number of M. bovis bacteria from the environment. However, the disease outbreak occurs when it emerges from infected cattle population. Moreover, the results show that if bTB emerges from infected humans, cattle, dairy product and environment at the same time, then there is disease outbreak. Thus, any intervention measure that targets on reducing number of infected cattle will have significant impact to contain bTB in human and cattle populations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. Prediction and control of cholera outbreak: Study case of Cameroon.
- Author
-
Hameni Nkwayep, C., Glèlè Kakaï, R., and Bowong, S.
- Subjects
PREVENTION of cholera ,VIBRIO cholerae ,KALMAN filtering ,MATHEMATICAL models - Abstract
This paper deals with the problem of the prediction and control of cholera outbreak using real data of Cameroon. We first develop and analyze a deterministic model with seasonality for the cholera, the novelty of which lies in the incorporation of undetected cases. We present the basic properties of the model and compute two explicit threshold parameters R
0 and R0 that bound the effective reproduction number R0 , from below and above, that is R0 ≤ R0 ≤ R0 . We prove that cholera tends to disappear when R0 ≤ 1, while when R0 >1, cholera persists uniformly within the population. After, assuming that the cholera transmission rates and the proportions of newly symptomatic are unknown, we develop the EnKf approach to estimate unmeasurable state variables and these unknown parameters using real data of cholera from 2014 to 2022 in Cameroon. We use this result to estimate the upper and lower bound of the effective reproduction number and reconstructed active asymptomatic and symptomatic cholera cases in Cameroon, and give a short-term forecasts of cholera in Cameroon until 2024. Numerical simulations show that (i) the transmission rate from free Vibrio cholerae in the environment is more important than the human transmission and begin to be high few week after May and in October, (ii) 90% of newly cholera infected cases that present the symptoms of cholera are not diagnosed and (iii) 60.36% of asymptomatic are detected at 14% and 86% of them recover naturally. The future trends reveals that an outbreak appeared from July to November 2023 with the number of cases reported monthly peaked in October 2023. An impulsive control strategy is incorporated in the model with the aim to avoid or prevent the cholera outbreak. In the first year of monitoring, we observed a reduction of more than 75% of incidences and the disappearance of the peaks when no control are available in Cameroon. A second monitoring of control led to a further reduction of around 60% of incidences the following year, showing how impulse control could be an effective means of eradicating cholera. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
40. The impact of demography in a model of malaria with transmission‐blocking drugs.
- Author
-
Ouifki, Rachid, Banasiak, Jacek, and Tchoumi, Stéphane Yanick
- Subjects
- *
BASIC reproduction number , *DEMOGRAPHY , *DISEASE eradication , *MALARIA , *INFECTIOUS disease transmission , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
In this paper, we develop and analyze a mathematical model for spreading malaria, including treatment with transmission‐blocking drugs (TBDs). The paper's main aim is to demonstrate the impact the chosen model for demographic growth has on the disease's transmission and the effect of its treatment with TBDs. We calculate the model's control reproduction number and equilibria and perform a global stability analysis of the disease‐free equilibrium point. The mathematical analysis reveals that, depending on the model's demography, the model can exhibit forward, backward, and even some unconventional types of bifurcation, where disease elimination can occur for both small and large values of the reproduction number. We also conduct a numerical analysis to explore the short‐time behavior of the model. A key finding is that for one type of demographic growth, the population experienced a significantly higher disease burden than the others, and when exposed to high levels of treatment with TBDs, only this population succeeded in effectively eliminating the disease within a reasonable timeframe. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. Bifurcation analysis and chaos in a discrete Hepatitis B virus model.
- Author
-
Khan, Abdul Qadeer, Bibi, Fakhra, and Aldosary, Saud Fahad
- Subjects
HEPATITIS B virus ,BASIC reproduction number ,REPRODUCTION ,INFECTIOUS disease transmission ,BIFURCATION theory ,STABILITY theory - Abstract
In this paper, we have delved into the intricate dynamics of a discrete-time Hepatitis B virus (HBV) model, shedding light on its local dynamics, topological classifications at equilibrium states, and pivotal epidemiological parameters such as the basic reproduction number. Our analysis extended to exploring convergence rates, control strategies, and bifurcation phenomena crucial for understanding the behavior of the HBV system. Employing linear stability theory, we meticulously examined the local dynamics of the HBV model, discerning various equilibrium states and their topological classifications. Subsequently, we identified bifurcation sets at these equilibrium points, providing insights into the system’s stability and potential transitions. Further, through the lens of bifurcation theory, we conducted a comprehensive bifurcation analysis, unraveling the intricate interplay of parameters that govern the HBV model’s behavior. Our investigation extended beyond traditional stability analysis to explore chaos and convergence rates, enriching our understanding of the dynamics of the understudied HBV model. Finally, we validated our theoretical findings through numerical simulations, confirming the robustness and applicability of our analysis in real-world scenarios. By integrating biological and epidemiological insights into our mathematical framework, we offered a holistic understanding of the dynamics of HBV transmission dynamics, with implications for public health interventions and disease control strategies. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. SIRS epidemic modeling using fractional-ordered differential equations: Role of fear effect.
- Author
-
Mangal, Shiv, Misra, O. P., and Dhar, Joydip
- Subjects
DIFFERENTIAL equations ,FRACTIONAL differential equations ,EPIDEMICS ,HOPF bifurcations ,COMMUNICABLE diseases ,BASIC reproduction number ,CLASSICAL swine fever - Abstract
In this paper, an SIRS epidemic model using Grunwald–Letnikov fractional-order derivative is formulated with the help of a nonlinear system of fractional differential equations to analyze the effects of fear in the population during the outbreak of deadly infectious diseases. The criteria for the spread or extinction of the disease are derived and discussed on the basis of the basic reproduction number. The condition for the existence of Hopf bifurcation is discussed considering fractional order as a bifurcation parameter. Additionally, using the Grunwald–Letnikov approximation, the simulation is carried out to confirm the validity of analytic results graphically. Using the real data of COVID-19 in India recorded during the second wave from 15 May 2021 to 15 December 2021, we estimate the model parameters and find that the fractional-order model gives the closer forecast of the disease than the classical one. Both the analytical results and numerical simulations presented in this study suggest different policies for controlling or eradicating many infectious diseases. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
43. Traveling wave solutions in a nonlocal dispersal SIR epidemic model with nonlocal time-delay and general nonlinear incidences.
- Author
-
Wu, Weixin and Zhang, Wenhui
- Subjects
BASIC reproduction number ,EPIDEMICS - Abstract
This paper investigates a nonlocal dispersal epidemic model under the multiple nonlocal distributed delays and nonlinear incidence effects. First, the minimal wave speed c ∗ and the basic reproduction number R 0 are defined, which determine the existence of traveling wave solutions. Second, with the help of the upper and lower solutions, Schauder's fixed point theorem, and limiting techniques, the traveling waves satisfying some asymptotic boundary conditions are discussed. Specifically, when ℛ 0 > 1 , for every speed c > c ∗ there exists a traveling wave solution satisfying the boundary conditions, and there is no such traveling wave solution for any 0 < c < c ∗ when ℛ 0 > 1 or c > 0 when ℛ 0 < 1. Finally, we analyze the effects of nonlocal time delay on the minimum wave speed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
44. Analysis of a reaction–diffusion dengue model with vector bias on a growing domain.
- Author
-
Wang, Jinliang, Qu, Hao, and Ji, Desheng
- Subjects
BASIC reproduction number ,DENGUE ,LYAPUNOV functions ,SPATIAL systems ,INFECTIOUS disease transmission ,FENITROTHION - Abstract
In this paper, we consider a reaction–diffusion dengue model on a varying domain that monotonically increases in time and gradually approaches saturation arising from environmental change. By the upper and lower solutions, comparison principle, asymptotic autonomous semiflows and the technique of Lyapunov function, we investigate the stabilities of equilibria in terms of the basic reproduction number $ \Re _0^{\rho } $ ℜ 0 ρ . The results show that (i) if $ \Re _0^{\rho } \gt 1 $ ℜ 0 ρ > 1 , the nontrivial solutions starting from the upper and lower solutions of the model approach to the set formulated by the maximal and minimal solutions of its related elliptic problem; (ii) the disease-free equilibrium is globally asymptotically stable when $ \Re _0^{\rho } \lt 1 $ ℜ 0 ρ < 1. Comparing our problem in different settings including growing domain, fixed domain and without spatial structure, our results demonstrate that the disease can spread in the growing domain, while vanish in the fixed domain; and the spatial model decreases the transmission risk compared with the system without spatial structure. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
45. Underdetection in a stochastic SIR model for the analysis of the COVID-19 Italian epidemic
- Author
-
Antonio Pievatolo, Fabrizio Ruggeri, Antonella Bodini, and Sara Pasquali
- Subjects
Original Paper ,Environmental Engineering ,Coronavirus disease 2019 (COVID-19) ,Computer science ,Susceptible-infected-removed ,Underdetection ,Model parameters ,Computational intelligence ,Interval (mathematics) ,Infection fatality rate ,Basic reproduction number ,Stochastic differential equation ,State-space SDE ,Econometrics ,Environmental Chemistry ,Identifiability ,Safety, Risk, Reliability and Quality ,Epidemic model ,General Environmental Science ,Water Science and Technology - Abstract
We propose a way to model the underdetection of infected and removed individuals in a compartmental model for estimating the COVID-19 epidemic. The proposed approach is demonstrated on a stochastic SIR model, specified as a system of stochastic differential equations, to analyse data from the Italian COVID-19 epidemic. We find that a correct assessment of the amount of underdetection is important to obtain reliable estimates of the critical model parameters. The adaptation of the model in each time interval between relevant government decrees implementing contagion mitigation measures provides short-term predictions and a continuously updated assessment of the basic reproduction number.
- Published
- 2021
46. Comments on “A Mathematical Study to Control Visceral Leishmaniasis: An Application to South Sudan”.
- Author
-
Iboi, E., Okuneye, K., Sharomi, O., and Gumel, A. B.
- Subjects
VISCERAL leishmaniasis ,MATHEMATICAL analysis ,BASIC reproduction number ,DISEASE vectors ,BIFURCATION theory - Abstract
Deterministic (ordinary differential equation) models for the transmission dynamics of vector-borne diseases that incorporate disease-induced death in the host(s) population(s) are generally known to exhibit the phenomenon of backward bifurcation (where a stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number of the model is less than unity). Further, it is well known that, in these models, the phenomenon of backward bifurcation does not occur when the disease-induced death rate is negligible (e.g., if the disease-induced death rate is set to zero). In a recent paper on the transmission dynamics of visceral leishmaniasis (a disease vectored by sandflies), titled “
A Mathematical Study to Control Visceral Leishmaniasis: An Application to South Sudan ,” published in Bulletin of Mathematical Biology, Vol. 79, Pages 1110-1134, 2017, Ghosh et al. (2017 ) stated that their deterministic model undergoes a backward bifurcation even when the disease-induced mortality in the host population is set to zero. This result is contrary to the well-established theory on the dynamics of vector-borne diseases. In this short note, we illustrate some of the key errors in the Ghosh et al. (2017 ) study. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
47. COVID-19 pandemic in India: a mathematical model study
- Author
-
Susmita Sarkar, Sudhanshu Kumar Biswas, Uttam Ghosh, and Jayanta Kumar Ghosh
- Subjects
Coronavirus disease 2019 (COVID-19) ,Prevention measure ,49J15 ,Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ,Aerospace Engineering ,Ocean Engineering ,Disease ,Asymptomatic class ,01 natural sciences ,Infection disease ,37N25 ,Environmental health ,92D30 ,0103 physical sciences ,Pandemic ,Electrical and Electronic Engineering ,010301 acoustics ,Original Paper ,Applied Mathematics ,Mechanical Engineering ,Model study ,COVID-19 ,Outbreak ,Basic reproduction number ,Geography ,Control and Systems Engineering ,Scale (social sciences) ,Quarantine ,Sensitivity analysis ,biomaterials - Abstract
The present novel corona virus (2019-nCoV) infection has created a global emergency situation by spreading all over the world in a large scale within very short time period. The infection induced death rate is also very high. There is no vaccine or anti-viral medicine for such infection. So at this moment a major worldwide problem is that how we can control this pandemic. On the other hand, India is a high population density country, where the corona virus disease (COVID-19) has started to spread from $1^{st}$ week of March, 2020 in a significant number of COVID-19 positive cases. Due to this high population density human to human social contact rate is very high in India. So control of the pandemic COVID-19 in early stage is very urgent and challenging problem. Mathematical models are employed in this paper to study the COVID-19 dynamics, to identify the influential parameters and to find the proper prevention strategies to reduce the outbreak size. In this work, we have formulated a deterministic compartmental model to study the spreading of COVID-19 and estimated the model parameters by fitting the model with reported data of ongoing pandemic in India. Sensitivity analysis has been done to identify the key model parameters. The basic reproduction number has been estimated from actual data and the effective basic reproduction number has been studied on the basis of reported cases. Some effective preventive measures and their impacts on the disease dynamics have also been studied. Future trends of the disease transmission has been Predicted from our model with some control measures. Finally, the positive measures to control the disease have been summarized.
- Published
- 2020
48. Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model
- Author
-
Conghui Xu, Zhenzhen Lu, YangQuan Chen, and Yongguang Yu
- Subjects
2019-20 coronavirus outbreak ,Coronavirus disease 2019 (COVID-19) ,q-bio.PE ,Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ,Population ,Epidemic ,Aerospace Engineering ,Ocean Engineering ,Fractional order ,01 natural sciences ,Mathematical Sciences ,Engineering ,Peak prediction ,0103 physical sciences ,Statistics ,Electrical and Electronic Engineering ,education ,Generalized SEIR model ,010301 acoustics ,Equilibrium point ,Original Paper ,education.field_of_study ,Applied Mathematics ,Mechanical Engineering ,COVID-19 ,Outbreak ,Acoustics ,Infectious Diseases ,Good Health and Well Being ,Geography ,Control and Systems Engineering ,Basic reproduction number ,math.DS ,Isolated cases - Abstract
In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which divided the population into susceptible, exposed, infectious, quarantined, recovered and insusceptible individuals and has a basic guiding significance for the prediction of the possible outbreak of infectious diseases like the coronavirus disease in 2019 (COVID-19) and other insect diseases in the future. Firstly, some qualitative properties of the model are analyzed. The basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{ R }}_{0}$$\end{document}R0 is derived. When \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{ R }}_{0}1$$\end{document}R0>1, the endemic equilibrium point is also unique. Furthermore, some conditions are established to ensure the local asymptotic stability of disease-free and endemic equilibrium points. The trend of COVID-19 spread in the USA is predicted. Considering the influence of the individual behavior and government mitigation measurement, a modified SEIQRP model is proposed, defined as SEIQRPD model, which is divided the population into susceptible, exposed, infectious, quarantined, recovered, insusceptible and dead individuals. According to the real data of the USA, it is found that our improved model has a better prediction ability for the epidemic trend in the next two weeks. Hence, the epidemic trend of the USA in the next two weeks is investigated, and the peak of isolated cases is predicted. The modified SEIQRP model successfully capture the development process of COVID-19, which provides an important reference for understanding the trend of the outbreak.
- Published
- 2020
49. The spread and control of rumors in a multilingual environment
- Author
-
Zhiyong Yu, Jiarong Li, Haijun Jiang, Xuehui Mei, and Shuzhen Yu
- Subjects
Lyapunov stability ,Original Paper ,Rumor spreading ,Correctness ,Computer science ,Applied Mathematics ,Mechanical Engineering ,Distributed computing ,Continuous control ,Control (management) ,Heterogeneous network ,Aerospace Engineering ,Ocean Engineering ,Rumor ,01 natural sciences ,Event-triggered impulsive control ,Control and Systems Engineering ,0103 physical sciences ,Multilingual environment ,Electrical and Electronic Engineering ,010301 acoustics ,Basic reproduction number ,Control methods - Abstract
This paper studies the rumor propagation model with heterogeneous networks in a multilingual environment. Firstly, a rumor propagation model with two language spreaders, in which the immunologic mechanism is considered in the ignorant, is proposed on heterogeneous networks. Secondly, the basic reproduction number and the dynamic behaviors are analyzed by using the next-generation matrix method and Lyapunov stability theory, respectively. Moreover, two control strategies are designed to effectively suppress the spread of the rumor. The one is continuous control strategy. By applying real-time control to the spreaders, the rumor spreading time can be greatly reduced and the rumor can die out in a short time. The other is event-triggered impulsive control strategy, which can effectively reduce the consumption of resources and ensure the extinction of the rumor. Finally, the correctness of theoretical analysis and the feasibility of control methods are verified by numerical simulations.
- Published
- 2020
50. The fit and predict COVID-19 using an extended compartmental model in the context of Indonesia.
- Author
-
Siradjuddin, Indrazno, Ningrum, Bella Cahya, Agiska, Inta Nurkhaliza, Sumari, Arwin Datumaya Wahyudi, Syaifudin, Yan Watequlis, Asmara, Rosa Andrie, and Funabiki, Nobuo
- Subjects
- *
BASIC reproduction number , *COVID-19 pandemic , *EPIDEMIOLOGICAL models , *COVID-19 , *VIRAL transmission - Abstract
In a pandemic outbreak such as COVID-19, that spreads widely around the world requires in depth research to predict the pattern of its spread and strategies to reduce the number of spreads. Predictive control is a mathematical approach to control systems where a model is used to make predictions about the future behavior of a system, and these predictions are then used to determine the control actions that should be taken. Based on these predictions, control measures such as lockdowns and social distancing could be optimized to reduce the spread of the virus and minimize its impact. A dynamic model is needed for quick and precise handling decisions. Mathematical models Epidemiology can be used in various fields, the implementation of which is COVID-19. The presentation of a dynamical system can use the basic compartment model, in which critical 퐶 and death 풟 states are considered, addressing more possibilities of mutual transitions between compartment states. 풮ℰℐℛ풞풟 estimates and forecasts the COVID-19 spread under uncertainties and constraints. This paper focuses on This paper focuses on fit and predict the 풮ℰℐℛ풞풟 model with time dependent basic reproduction numbers and health resource-dependent death rates to real COVID-19 data in Indonesia. Data have been collected for a specific period of time, the best-fitting parameters have been obtained, and the changes in the basic reproduction number over time have been estimated. The presented model has included the transition probability of the infected state to the critical state and the transition probability of the critical state to the death state, based on different age groups, so that the number of hospital beds has also been cooperative in computing the compartment states. Using the best-fitting parameters of the 풮ℰℐℛ풞풟 model, the development of the compartment states in the near future was estimated. The simulation result shows that the obtained parameters of the 풮ℰℐℛ풞풟 model were reasonably satisfying where the simulated states from the model could fit the real data with a small degree of error so that it can be used to predict the path of further deployment. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.