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2. COVID-19 and India: what next?
- Author
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Behl, Ramesh and Mishra, Manit
- Published
- 2021
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3. Forecasting the impact of epidemic outbreaks on the supply chain: modelling asymptomatic cases of the COVID-19 pandemic.
- Author
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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
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4. New Challenges in the Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-Pharmaceutical Actions and Vaccination Strategies.
- Author
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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
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5. Dynamical analysis of a spatio-temporal model encompassing the avian flu transmission in human population.
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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
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6. Dynamics of a linear source epidemic system with diffusion and media impact.
- Author
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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
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7. Dynamic analysis and optimal control of knowledge diffusion model in regional innovation ecosystem under digitalization.
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He, Zitong, Wang, Haijun, Hu, Yuhan, Ma, Xiaolin, and Zhao, Huiyan
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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
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8. Mathematical analysis of an SIQR model with non-linear incidence and saturated treatment rates.
- Author
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Yadavt, Sudha, Bhadauria, Archana Singh, and Verma, Vijai Shanker
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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
9. SIRS Epidemic Models with Delays, Partial and Temporary Immunity and Vaccination.
- Author
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Chen-Charpentier, Benito
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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
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10. Dynamics analysis of a reaction-diffusion malaria model accounting for asymptomatic carriers.
- Author
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Shi, Yangyang, Chen, Fangyuan, Wang, Liping, and Zhang, Xuebing
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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
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11. Quantitative analysis of a fractional order of the $ SEI_{c}\, I_{\eta} VR $ epidemic model with vaccination strategy.
- Author
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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
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- View/download PDF
12. Modeling the impact of non-human host predation on the transmission of Chagas disease.
- Author
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Dai X, Wu X, Jiang J, and Rong L
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- 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
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13. Global stability and optimal control of an age-structured SVEIR epidemic model with waning immunity and relapses.
- Author
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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
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14. Prevention and control of Ebola virus transmission: mathematical modelling and data fitting.
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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
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15. A mathematical model of COVID-19 with multiple variants of the virus under optimal control in Ghana.
- Author
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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
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16. A hybrid Lagrangian-Eulerian model for vector-borne diseases.
- Author
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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
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17. A simulation-based approach for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data.
- Author
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Ogi-Gittins I, Hart WS, Song J, Nash RK, Polonsky J, Cori A, Hill EM, and Thompson RN
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- 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
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18. Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic
- Author
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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
19. The fit and predict COVID-19 using an extended compartmental model in the context of Indonesia.
- Author
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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
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- View/download PDF
20. Complex dynamics of an epidemic model with saturated media coverage and recovery
- Author
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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
21. Exploring the influence of burial and cremation practices on Nipah virus transmission: a SIRD model analysis
- Author
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Kubra, Khadija Tul, Gulshan, Samra, and Ali, Rooh
- Published
- 2024
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- 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
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Chhetri, Bishal, Vamsi, D. K. K., and Sanjeevi, Carani B
- Published
- 2024
- Full Text
- View/download PDF
23. Dynamics in a delayed rumor propagation model with logistic growth and saturation incidence.
- Author
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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
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- View/download PDF
24. Modeling and analysis of Cystic Echinococcosis epidemic model with health education.
- Author
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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
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- View/download PDF
25. Analyzing the Asymptotic Behavior of an Extended SEIR Model with Vaccination for COVID-19.
- Author
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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
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- View/download PDF
26. A discrete SIS-model built on the strictly positive scheme.
- Author
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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
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- View/download PDF
27. ON THE STABILITY ANALYSIS OF A FRACTIONAL ORDER EPIDEMIC MODEL INCLUDING THE GENERAL FORMS OF NONLINEAR INCIDENCE AND TREATMENT FUNCTION.
- Author
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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
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- View/download PDF
28. The spatiotemporal transmission dynamics of COVID-19 among multiple regions: a modeling study in Chinese provinces
- Author
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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
29. Dynamical analysis of a heroin–cocaine epidemic model with nonlinear incidence and spatial heterogeneity.
- Author
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Xu, Jinhu
- Subjects
HEROIN ,BASIC reproduction number ,GLOBAL asymptotic stability ,HETEROGENEITY ,EPIDEMICS ,DOPAMINE - Abstract
In this paper, we investigated a new heroin–cocaine epidemic model which incorporates spatial heterogeneity and nonlinear incidence rate. The main project of this paper is to explore the threshold dynamics in terms of the basic reproduction number $ \mathcal {R}_0 $ R 0 , which was defined by applying the next-generation operator. The threshold type results shown that if $ \mathcal {R}_0 \lt 1 $ R 0 < 1 , then the drug-free steady state is globally asymptotically stable. If $ \mathcal {R}_0 \gt 1 $ R 0 > 1 , then heroin–cocaine spread is uniformly persistent. Furthermore, the globally asymptotic stability of the drug-free steady state has been established for the critical case of $ \mathcal {R}_0=1 $ R 0 = 1 by analysing the local asymptotic stability and global attractivity. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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- View/download PDF
30. Modelling the impact of precaution on disease dynamics and its evolution.
- Author
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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
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- View/download PDF
31. Threshold dynamics of a reaction-advection-diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity.
- Author
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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
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32. Transmission dynamics of a reaction-advection-diffusion dengue fever model with seasonal developmental durations and intrinsic incubation periods.
- Author
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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
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- View/download PDF
33. A novel within-host model of HIV and nutrition.
- Author
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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
34. Approximating reproduction numbers: a general numerical method for age-structured models.
- Author
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Reggi S, Scarabel F, and Vermiglio R
- Subjects
- Humans, Communicable Diseases epidemiology, Communicable Diseases transmission, Population Dynamics, Epidemics statistics & numerical data, Algorithms, Age Factors, Models, Biological, Basic Reproduction Number statistics & numerical data, Computer Simulation
- Abstract
In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases.
- Published
- 2024
- Full Text
- View/download PDF
35. 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
36. 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
37. 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
38. 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
39. 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
40. The impact of temperature, humidity and closing school on the mumps epidemic: a case study in the mainland of China.
- Author
-
Li, Xiaoqun, Zhang, Lianyun, Tan, Changlei, Wu, Yan, Zhang, Ziheng, Ding, Juan, and Li, Yong
- Subjects
SCHOOL closings ,MUMPS ,BASIC reproduction number ,VACCINATION coverage ,HUMIDITY ,SCHOOL bullying ,VIOLENCE in the community - Abstract
Background: To control resurging infectious diseases like mumps, it is necessary to resort to effective control and preventive measures. These measures include increasing vaccine coverage, providing the community with advice on how to reduce exposure, and closing schools. To justify such intervention, it is important to understand how well each of these measures helps to limit transmission. Methods: In this paper, we propose a simple SEILR (susceptible-exposed-symptomatically infectious-asymptomatically infectious-recovered) model by using a novel transmission rate function to incorporate temperature, humidity, and closing school factors. This new transmission rate function allows us to verify the impact of each factor either separately or combined. Using reported mumps cases from 2004 to 2018 in the mainland of China, we perform data fitting and parameter estimation to evaluate the basic reproduction number R 0 . As a wide range of one-dose measles, mumps, and rubella (MMR) vaccine programs in China started only in 2008, we use different vaccination proportions for the first Stage I period (from 2004 to 2008) and the second Stage II period (from 2009 to 2018). This allows us to verify the importance of higher vaccine coverage with a possible second dose of MMR vaccine. Results: We find that the basic reproduction number R 0 is generally between 1 and 3. We then use the Akaike Information Criteria to assess the extent to which each of the three factors contributed to the spread of mumps. The findings suggest that the impact of all three factors is substantial, with temperature having the most significant impact, followed by school opening and closing, and finally humidity. Conclusion: We conclude that the strategy of increasing vaccine coverage, changing micro-climate (temperature and humidity), and closing schools can greatly reduce mumps transmission. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. Dynamics of Infectious Diseases Incorporating a Testing Compartment.
- Author
-
Yang, Chayu and Deng, Bo
- Subjects
BASIC reproduction number ,COMMUNICABLE diseases ,EQUILIBRIUM testing ,SARS-CoV-2 ,COVID-19 pandemic ,MEDICAL model - Abstract
In this paper, we construct an infectious disease model with a testing compartment and analyze the existence and stability of its endemic states. We obtain the basic reproduction number, R 0 , and demonstrate the existence of one endemic equilibrium without testing and one endemic equilibrium with testing and prove their local and global stabilities based on the value of the basic reproduction number, R 0 . We then apply our model to the US COVID-19 pandemic and find that, for a large parameter set, including those relevant to the SARS-CoV-2 virus, our analytic and numerical results suggest that the trajectories will be trapped to the testing-free state when the testing number is small enough. This indicates that the pandemic may end with a testing-free endemic state through a novel and surprising mechanism called stochastic trapping. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. Stability analysis for a HIV model with cell-to-cell transmission, two immune responses and induced apoptosis.
- Author
-
Ru Meng, Yantao Luo, and Tingting Zheng
- Subjects
GLOBAL asymptotic stability ,BASIC reproduction number ,HOPFIELD networks ,IMMUNE response ,APOPTOSIS ,HIV - Abstract
In this paper, a dynamic HIV model with cell-to-cell transmission, two immune responses, and induced apoptosis is proposed and studied. First, the non-negativity and boundedness of the solutions of the model are given, and then the exact expression of the basic reproduction number R0 is obtained by using the next generation matrix method. Second, criteria are obtained for the local stability of the disease-free equilibrium, immune response-free equilibrium, and the infected equilibrium with both humoral and cellular immune responses. Furthermore, the threshold conditions are also derived for the global asymptotic stability of the disease-free equilibrium, immune responsefree equilibrium, and the infected equilibrium with both humoral and cellular immune responses by constructing the suitable Lyapunov function. Finally, some numerical simulations are conducted to verify the theoretical results; the numerical simulation results show that the increase of apoptosis rate had a positive role in the control of viral infection. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
43. An age-structured SIPC model of cervical cancer with immunotherapy.
- Author
-
Sari, Eminugroho Ratna, Aryati, Lina, and Adi-Kusumo, Fajar
- Subjects
CERVICAL cancer ,REPRODUCTION ,IMMUNOTHERAPY ,BASIC reproduction number ,HUMAN papillomavirus ,PARTIAL differential equations - Abstract
Immunotherapy is a targeted therapy that can be applied to cervical cancer patients to prevent DNA damage caused by human papillomavirus (HPV). The HPV infects normal cervical cells withing a specific cell age interval, i.e., between the G1 to S phase of the cell cycle. In this study, we developed a new mathematical model of age-dependent immunotherapy for cervical cancer. The model is a four-dimensional first-order partial differential equation with time- and age-independent variables. The cell population is divided into four sub-populations, i.e., susceptible cells, cells infected by HPV, precancerous cells, and cancer cells. The immunotherapy term has been added to precancerous cells since these cells can experience regression if appointed by proper treatments. The immunotherapy process is closely related to the rate of T-cell division. The treatment works in the same cell cycle that stimulates and inhibits the immune system. In our model, immunotherapy is represented as a periodic function with a small amplitude. It is based on the fluctuating interaction between Tcells and precancerous cells. We have found that there are two types of steady-state conditions, i.e., infection-free and endemic. The local and global stability of an infection-free steady-state has been analyzed based on basic reproduction numbers. We have solved the Riccati differential equation to show the existence of an endemic steady-state. The stability analysis of the endemic steady-state has been determined by using the perturbation approach and solving integral equations. Some numerical simulations are also presented in this paper to illustrate the behavior of the solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
44. Dynamical analysis of an age-structured SEIR model with relapse.
- Author
-
NABTi, Abderrazak
- Subjects
BASIC reproduction number ,LATENT infection ,INFECTIOUS disease transmission ,STABILITY theory ,DIFFERENTIAL equations - Abstract
Mathematical models play a crucial role in controlling and preventing the spread of diseases. Based on the communication characteristics of diseases, it is necessary to take into account some essential epidemiological factors such as the time delay that takes an individual to progress from being latent to become infectious, the infectious age which refers to the duration since the initial infection and the occurrence of reinfection after a period of improvement known as relapse, etc. Moreover, age-structured models serve as a powerful tool that allows us to incorporate age variables into the modeling process to better understand the effect of these factors on the transmission mechanism of diseases. In this paper, motivated by the above fact, we reformulate an SEIR model with relapse and age structure in both latent and infected classes. Then, we investigate the asymptotic behavior of the model by using the stability theory of differential equations. For this purpose, we introduce the basic reproduction number R 0 of the model and show that this threshold parameter completely governs the stability of each equilibrium of the model. Our approach to show global attractivity is based on the fluctuation lemma and Lyapunov functionals method with some results on the persistence theory. The conclusion is that the system has a disease-free equilibrium which is globally asymptotically stable if R 0 < 1 , while it has only a unique positive endemic equilibrium which is globally asymptotically stable whenever R 0 > 1 . Our results imply that early diagnosis of latent infection with decrease in both transmission and relapse rates may lead to control and restrict the spread of disease. The theoretical results are illustrated with numerical simulations, which indicate that the age variable is an essential factor affecting the spread of the epidemic. [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
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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
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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. Dynamics of spatio-temporal HIV–AIDS model with the treatments of HAART and immunotherapy
- Author
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Ghani, Mohammad
- Published
- 2024
- Full Text
- View/download PDF
48. Threshold dynamics of an uncertain SIRS epidemic model with a bilinear incidence.
- Author
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Tan, Simin, Zhang, Ling, and Sheng, Yuhong
- Subjects
BASIC reproduction number ,INFECTIOUS disease transmission ,EPIDEMICS ,ORDINARY differential equations ,COMMUNICABLE diseases ,DISEASE outbreaks - Abstract
This paper mainly discusses the extinction and persistent dynamic behavior of infectious diseases with temporary immunity. Considering that the transmission process of infectious diseases is affected by environmental fluctuations, stochastic SIRS models have been proposed, while the outbreak of diseases is sudden and the interference terms that affect disease transmission cannot be qualified as random variables. Liu process is introduced based on uncertainty theory, which is a new branch of mathematics for describing uncertainty phenomena, to describe uncertain disturbances in epidemic transmission. This paper first extends the classic SIRS model from a deterministic framework to an uncertain framework and constructs an uncertain SIRS infectious disease model with constant input and bilinear incidence. Then, by means of Yao-Chen formula, α-path of uncertain SIRS model and the corresponding ordinary differential equations are obtained to introduce the uncertainty threshold function R 0 * as the basic reproduction number. Moreover, two equilibrium states are derived. A series of numerical examples show that the larger the value of R 0 * , the more difficult it is to control the disease. If R 0 * ≤ 1 , the infectious disease will gradually disappear, while if R 0 * > 1 , the infectious disease will develop into a local epidemic. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. The SEIR Covid-19 model described by fractional-order difference equations: analysis and application with real data in Brazil.
- Author
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Almatroud, A. Othman, Djenina, Noureddine, Ouannas, Adel, and Grassi, Giuseppe
- Subjects
DIFFERENCE equations ,COVID-19 ,EPIDEMIOLOGICAL models ,BASIC reproduction number ,CAPABILITIES approach (Social sciences) ,GLOBAL analysis (Mathematics) - Abstract
Several efforts have been recently devoted to the studies on epidemic mathematical models based on fractional-order operators, by virtue of their capability to take into account memory effects and nonlocal features. The aim of this paper is to make a contribution to the topic by introducing a novel Covid-19 model described by non-integer-order difference equations. By conducting a stability analysis, the paper shows that the conceived system has two fixed points at most, i.e. a disease-free fixed point and an endemic fixed point. In particular, a theorem is proved, which assures the global stability of the disease-free fixed point, indicating that the pandemic will disappear when a simple condition on the system parameters is satisfied. Finally, simulation results are carried out with the aim to highlight the capability of the conceived approach. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
50. Analysis on a spatial SIS epidemic model with saturated incidence function in advective environments: II. Varying total population.
- Author
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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
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