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This paper presents globally numerical properties of a new numerical scheme for a reaction-diffusion advection susceptible-infected-susceptible (SIS) model. A new numerical treatment technique is introduced in spatial discretization of advection-diffusion equation, which enables the numerical solutions to preserve the stability and positivity with less stepsize restrictions. The convergence, biological significance and globally stability of numerical solutions is explored in the paper. A threshold value, named by numerical basic reproduction number and denoted by R 0 Δ x , is introduced in the numerical stability analysis of the model. It is proved the numerical disease free equilibrium (DFE) is globally asymptotically stable if R 0 Δ x < 1 and unstable if R 0 Δ x > 1. It is shown the numerical basic number R 0 Δ x replicates the asymptotic behaviors of the basic reproduction number R 0 for the model. Some numerical experiments are given in the end to confirm the conclusions. [ABSTRACT FROM AUTHOR]

• Proposed a new switched epidemic model arising from changes in contact rates in an infected society. • Considering vulnerable individuals as vaccination frontiers along with the possibility of vaccine failure. • Qualitative analysis of the model using two theorems on positive invariance set and positivity of solutions. • Global stability analysis of equilibria, with a focus on the basic reproduction number (R 0) as a bifurcation value. • Manipulating the contact rates between subsystems through the contact-rate-dependent average dwell time to control a disease. This paper introduces a switched SQWVEAIR (Susceptible, Quarantined, Weak, Vaccinated, Exposed, Asymptomatic, Infected, and Recovered) epidemic model considering changing contact rates in an infected society. It also takes into account the presence of vulnerable individuals as frontiers in vaccination, recognizing their societal importance. The qualitative analysis of the model involves two theorems on the positive invariance set and the positivity of the solutions. Additionally, it calculates the equilibria of the proposed model and analyzes their global stabilities using the Lyapunov functional technique, focusing on the basic reproduction number (R 0) as a bifurcation value. To achieve globally uniformly exponential stability, it calculates the contact-rate-dependent average dwell time (CRDADT) for each stable and unstable subsystem, developing a Lyapunov function. It also derives sufficient conditions, expressed as linear matrix inequalities (LMIs), to ensure stability. A numerical example is provided to demonstrate the effectiveness of the theoretical analysis and validate our research findings. [ABSTRACT FROM AUTHOR]

The recent experimental results illustrate that adding ivermectin to artemisinin-based combination therapy can target malaria parasite and its vector, which may be a new treatment option. In this paper, we present a new malaria transmission model, which incorporates spatial heterogeneity, general incidence rate and treatment plan with ivermectin. The basic reproduction number R 0 is introduced as a threshold parameter to determine whether malaria will eventually die out or not. Further, we propose and analyze the regional optimal control problem to minimize mosquito population, exposed and infectious humans as well as cost. Numerically, we investigate the transmission and control of malaria in The Gambia. Results show that the treatment plans with ivermectin and without ivermectin have the same contribution to R 0 , but have different effects on the epidemic level of malaria. This conclusion also holds for different incidence rates with some assumptions. Moreover, by comparing the cost and benefit of different strategies, the most cost-effective strategy is found. • A malaria model includes spatial heterogeneity, general incidence rate and ivermectin therapy. • Regional optimal control problem with terminal state in objective is investigated. • The transmission and control of malaria in The Gambia are discussed. • The effects of mosquito species distribution and incidence rate are explored. • The most cost-effective strategy is determined by comparing cost and benefit of eleven strategies. [ABSTRACT FROM AUTHOR]

Considering the decay of information with time, this paper proposes a rumour propagation model based on information intervention. Applying optimal control and stochastic noise propagation, we explain the influence of the information intervention mechanism on the dynamics of rumour propagation. First, we calculate the equilibrium points and basic reproduction number of our model. Second, this paper selects the intensity of information intervention and the control rate of spreaders as control variables and explores the dynamics of rumour propagation in deterministic and stochastic systems under optimal control. Finally, to support the theoretical results, we verify the stationarity condition through numerical simulation and analyse the changes in different populations. Additionally, we compare the performance of the deterministic and stochastic models to each other, as well as with existing models. [ABSTRACT FROM AUTHOR]

• When individuals send anti-epidemic signals, the government will adopt restrictive policies under budget surplus or balance. • When individuals send freedom signals, the government chooses not to implement restrictive policies. • When governments choose not to impose restrictions, the epidemic development depends on its properties. • When the government chooses to implement restrictive policies, the epidemic development depends on how strict the policies are. The ongoing COVID-19 pandemic imposes serious short-term and long-term health costs on populations. Restrictive government policy measures decrease the risks of infection, but produce similarly serious social, mental health, and economic problems. Citizens have varying preferences about the desirability of restrictive policies, and governments are thus forced to navigate this tension in making pandemic policy. This paper analyses the situation facing government using a game-theoretic epidemiological model. We classify individuals into health-centered individuals and freedom-centered individuals to capture the heterogeneous preferences of citizens. We first use the extended Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) model (adding individual preferences) and the signaling game model (adding government) to analyze the strategic situation against the backdrop of a realistic model of COVID-19 infection. We find the following: 1. There exists two pooling equilibria. When health-centered and freedom-centered individuals send anti-epidemic signals, the government will adopt strict restrictive policies under budget surplus or balance. When health-centered and freedom-centered individuals send freedom signals, the government chooses not to implement restrictive policies. 2. When governments choose not to impose restrictions, the extinction of an epidemic depends on whether it has a high infection transmission rate; when the government chooses to implement non-pharmacological interventions (NPIs), whether an epidemic will disappear depends on how strict the government's restrictions are. Based on the existing literature, we add individual preferences and put the government into the game as a player. Our research extends the current form of combining epidemiology and game theory. By using both we get a more realistic understanding of the spread of the virus and combine that with a richer understanding of the strategic social dynamics enabled by game theoretic analysis. Our findings have important implications for public management and government decision-making in the context of COVID-19 and for potential future public health emergencies. [ABSTRACT FROM AUTHOR]

Global efforts are focused on discussing effective measures for minimizing the impact of COVID-19 on global community. It is clear that the ongoing pandemic of this virus caused an immense threat to public health and economic development. Mathematical models with real data simulations are powerful tools that can identify key factors of pandemic and improve control or mitigation strategies. Compared with integer-order and left-hand side fractional models, two-side fractional models can better capture the state of pandemic spreading. In this paper, two-side fractional models are first proposed to qualitative and quantitative analysis of the COVID-19 pandemic. A basic framework are given for the prediction and analysis of infectious diseases by these types of models. By means of asymptotic stability analysis of disease-free and endemic equilibrium points, basic reproduction number R 0 can be obtained, which is helpful for estimating the severity of an outbreak qualitatively. Sensitivity analysis of R 0 is performed to identify and rank key epidemiological parameters. Based on the real data of the United States, numerical tests reveal that the model with both left-hand side fractional derivative and right-hand side fractional integral terms has a better forecast ability for the epidemic trend in the next ten days. Our extensive computational results also quantitatively reveal that non-pharmaceutical interventions, such as isolation, stay at home, strict control of social distancing, and rapid testing can play an important role in preventing the pandemic of the disease. Thus, the two-side fractional models are proposed in this paper can successfully capture the change rule of COVID-19, which provide a strong tool for understanding and analyzing the trend of the outbreak. [ABSTRACT FROM AUTHOR]

The key aim of this paper is to construct a modified version of the SEIQR essential disease dynamics model for the COVID-19 emergence. The modified SEIQR pandemic model takes a groundbreaking approach to evaluate and monitor the COVID-19 epidemic. The complex studies presented in this paper are based on real-world data from Saudi Arabia. A reproduction number and a systematic stability analysis are included in the new version of SEIQR model dynamics. Using the Jacobian linearization process, we can obtain the domain of the solution and the state of equilibrium based on the modified SEIQR model. The equilibrium and its importance have been identified, and the disease-free stability of the equilibrium has been investigated. The reproduction number was calculated using internal metrics, and the global stability of the current model's equilibrium was demonstrated using Lyapunov's stability theorem. To see how well the SEIQR proposed model went, it was compared to real COVID-19 spread data in Saudi Arabia. According to the results, the new SEIQR proposed model is a good match for researching the spread of epidemics like COVID-19. In the end, we presented an optimal protocol to prevent the dissemination of COVID-19. Staying at home and transporting sick people as far as possible to a safe region is the most effective strategy to prevent COVID-19 spread. It is critical to offer infected people safe and effective treatment, as well as antibiotics and nutrients to non-affected people. To detect confirmed infections, we must provide more effective and reliable diagnostic methods. Furthermore, increasing understanding of how to recognize the disease, its symptoms, and how to confirm the infection. [ABSTRACT FROM AUTHOR]

• A generalized mathematical model has been proposed to analysis COVID-19. • Deterministic and stochastic SIQR models with vaccination and treatment are studied. • Conditions for the extinction of the epidemic are obtained. • The theoretical results of model are verified by the epidemic data of Russia and Serbia. • We make the short-term prediction of COVID-19 in Russia and Serbia. In this paper, we propose and investigate the SIQR epidemic model with a generalized incidence rate function, a general treatment function and vaccination term. We firstly consider the existence and uniqueness of the global nonnegative solution to the deterministic model. Further, we show the locally asymptotic stability of the disease-free equilibrium and endemic equilibrium of the deterministic model, and obtain the basic reproduction number R 0. Then we study the existence and uniqueness of the global positive solution to the stochastic model with any positive initial value. Meanwhile, we obtain sufficient conditions for the extinction of the disease in the stochastic epidemic model, and find that the large noise can make the disease die out exponentially. Finally, we make an empirical analysis by the COVID-19 data of Russia and Serbia. By the performance comparison of different models, it shows that the model with vaccination and treatment we proposed is better for the real situation, which is also verified by different estimation methods. Especially, that shows the recovery rate of the infected increases by 0.042 and the death rate of the recovered is 1.525 times that of normal human in Russia. Through statistical analysis, the short-term trend of epidemic transmission is predicted: under the condition of unchanged prevention and control policies, it may reach a stable endemic equilibrium state in Russia and the epidemic will eventually extinct in Serbia. [ABSTRACT FROM AUTHOR]

In this paper, a novel fractional-order monkeypox epidemic model is introduced, where fractional-order derivatives in the sense of Caputo are applied to achieve more realistic results for the proposed nonlinear model. The newly developed model, which models the transmission and spread of monkeypox across the interacting populations of humans and rodents, is controlled by a 14-dimensional system of fractional-order differential equations. To comply with empirical and reported observations, the state variables of the proposed model are categorized into three main groups of state variables: the population who are at high risk of being infected, people with low infection probability, and finally, rodents who can carry and transmit the virus. The high-risk group represents individuals who might be more vulnerable to the virus due to their habits, workplace, or hygienic behaviors. The existence, uniqueness, non-negativity, and boundedness of the solution to the proposed model are proved. The next-generation matrix approach is used to determine the control monkeypox reproduction number, R 0 , and the equilibrium points for the proposed model are obtained. The effect of the main parameters in the model is thoroughly investigated to provide new insight into the new dynamics of the model. The region of stability of the disease-free points (DFE) is obtained in the space of parameters, and the effect of the parameters is examined. In addition, the optimal control strategy is applied to the model to provide insight into some prevention control to stop the disease from spreading and to provide new control strategies during the monkeypox outbreak. Numerical simulations are performed to validate the theoretical results of the different optimal control strategies. [ABSTRACT FROM AUTHOR]

• A multi-objective optimal reaction-diffusion model based on vaccination-isolation strategy is proposed. • Complex dynamic behaviors of the reaction-diffusion model are explored. • The functions of social cost, social benefit, and basic reproduction number are given. • The optimal path of COVID-19 control based on the basic reproduction number is determined. • The optimization of social cost, social benefit and basic reproduction number, based on vaccination-isolation is explored. In this paper, a reaction-diffusion COVID-19 model is proposed to explore how vaccination-isolation strategies affect the development of the epidemic. First, the basic dynamical properties of the system are explored. Then, the system's asymptotic distributions of endemic equilibrium under different conditions are studied. Further, the global sensitivity analysis of R 0 is implemented with the aim of determining the sensitivity for these parameters. In addition, the optimal vaccination-isolation strategy based on the optimal path is proposed. Meantime, social cost C (m , σ) , social benefit B (m , σ) , threshold R 0 (m , σ) three objective optimization problem based on vaccination-isolation strategy is explored, and the maximum social cost (M S C) and maximum social benefit (M S B) are obtained. Finally, the instance prediction of the Lhasa epidemic in China on August 7, 2022, is made by using the piecewise infection rates β 1 (t) , β 2 (t) , and some key indicators are obtained as follows: (1) The basic reproduction numbers of each stage in Lhasa, China are R 0 (1 : 8) = 0.4678 , R 0 (9 : 20) = 2.7655 , R 0 (21 : 30) = 0.3810 and R 0 (31 : 100) = 0.7819 ; (2) The daily new cases of this epidemic will peak at 43 on the 20th day (August 26, 2022); (3) The cumulative cases in Lhasa, China will reach about 640 and be cleared about the 80th day (October 28, 2022). Our research will contribute to winning the war on epidemic prevention and control. [ABSTRACT FROM AUTHOR]

[Display omitted] • A new and efficient fractional model is explored for the investigation of COVID-19 dynamics. • The associated dynamical behaviors are discussed in terms of equilibrium points, invariant region, etc. • To implement the proposed model numerically, an efficient approximation scheme is also employed. • Simulation results are compared with a real case of COVID-19 pandemic in Italy. • As a result, the new fractional model simulates the reality more precisely than the other classical frameworks. Mathematical modelling is a rapidly expanding field that offers new and interesting opportunities for both mathematicians and biologists. Concerning COVID-19, this powerful tool may help humans to prevent the spread of this disease, which has affected the livelihood of all people badly. The main objective of this research is to explore an efficient mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model in this paper is formulated in the Caputo sense, employs a nonlinear time-varying transmission rate, and consists of ten population classes including susceptible, infected, diagnosed, ailing, recognized, infected real, threatened, diagnosed recovered, healed, and extinct people. The existence of a unique solution is explored for the new model, and the associated dynamical behaviours are discussed in terms of equilibrium points, invariant region, local and global stability, and basic reproduction number. To implement the proposed model numerically, an efficient approximation scheme is employed by the combination of Laplace transform and a successive substitution approach; besides, the corresponding convergence analysis is also investigated. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic in Italy. By using these comparisons between the simulated and measured data, we find the best value of the fractional order with minimum absolute and relative errors. Also, the impact of different parameters on the spread of viral infection is analyzed and studied. According to the comparative results with real data, we justify the use of fractional concepts in the mathematical modelling, for the new non-integer formalism simulates the reality more precisely than the classical framework. [ABSTRACT FROM AUTHOR]

Recent field and experimental studies show that mobility patterns for humans exhibit scale-free nonlocal dynamics with heavy-tailed distributions characterized by Lévy flights. To study the long-range geographical spread of infectious diseases, in this paper we propose a susceptible-infectious-susceptible epidemic model with Lévy flights in which the dispersal of susceptible and infectious individuals follows a heavy-tailed jump distribution. Owing to the fractional diffusion described by a spectral fractional Neumann Laplacian, the nonlocal diffusion model can be used to address the spatiotemporal dynamics driven by the nonlocal dispersal. The primary focuses are on the existence and stability of disease-free and endemic equilibria and the impact of dispersal rates and fractional powers on the spatial profiles of these equilibria. A variational characterization of the basic reproduction number R 0 is obtained and its dependence on dispersal rates and fractional powers is also examined. Then R 0 is utilized to investigate the effects of spatial heterogeneity on the transmission dynamics. It is shown that R 0 serves as a threshold for determining the existence and nonexistence of an epidemic equilibrium as well as the stability of the disease-free and endemic equilibria. In particular, in low-risk regions both dispersal rates and fractional powers play a critical role and are capable of altering the threshold value. Numerical simulations were performed to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

• Collected papers on estimations of four epidemiological parameters regarding COVID-19. • Quantitatively compared and synthesized preprints and peer-reviewed publications. • Verified the validity of the COVID-19 parameter estimations of the preprints. • Synthesized parameters can effectively capture the patterns of COVID-19. We aimed to explore the collective wisdom of preprints related to COVID-19 by comparing and synthesizing them with results of peer-reviewed publications. PubMed, Google Scholar, medRxiv, bioRxiv, arXiv, and SSRN were searched for papers regarding the estimation of four epidemiological parameters of COVID-19: the basic reproduction number, incubation period, infectious period, and case-fatality-rate. Distributions of parameters and timeliness of preprints and peer-reviewed papers were compared. Four parameters in two groups were synthesized by bootstrapping, and their validities were evaluated by simulated cumulative cases of the susceptible-exposed-infectious-recovered-dead-cumulative (SEIRDC) model. A total of 106 papers were included for analysis. The distributions of four parameters in two literature groups were close, and the timeliness of preprints was better. Synthesized estimates of the basic reproduction number (3.18, 95% CI 2.85–3.53), incubation period (5.44 days, 95% CI 4.98–5.99), infectious period (6.25 days, 95% CI 5.09–7.51), and case-fatality-rate (4.51%, 95% CI 3.41%–6.29%) were obtained. Simulated cumulative cases of the SEIRDC model matched well with the onset cases in China. The validity of the COVID-19 parameter estimations of the preprints was on par with that of peer-reviewed publications, and synthesized results of literatures could reduce the uncertainty and be used for epidemic decision-making. [ABSTRACT FROM AUTHOR]

This paper considers the novel fractional-order operator developed by Atangana-Baleanu for transmission dynamics of the SARS-CoV-2 epidemic. Assuming the importance of the non-local Atangana-Baleanu fractional-order approach, the transmission mechanism of SARS-CoV-2 has been investigated while taking into account different phases of infection and various transmission routes of the disease. To conduct the proposed study, first of all, we shall formulate the model by using the classical operator of ordinary derivatives. We utilize the fractional order derivative and the model will be extended to a model containing fractional order derivatives. The operator being used is the fractional differential operator and has fractional order Φ 1 . The model is analyzed further and some basic aspects of the model are investigated besides calculating the basic reproduction number and the possible equilibria of the proposed model. The equilibria of the model are examined for stability purposes and necessary conditions for stability are obtained. Stability is also necessary in terms of numerical setup. The theory of non-linear functional analysis is employed and Ulam-Hyers's stability of the model is presented. The approach of newton's polynomial is considered and a new numerical scheme is developed which helped in presenting an iterative process for the proposed ABC system. Based on this scheme, sample curves are obtained for various values of Φ 1 and a pattern is derived between the dynamics of the infection and the order of the derivative. Further simulations are presented which show the cruciality and importance of various parameters and the impact of such parameters on the dynamics and control of the disease is presented. The findings of this study will also provide strong conceptual insights into the mechanisms of contagious diseases, assisting global professionals in developing control policies. [ABSTRACT FROM AUTHOR]

• A dengue model is proposed with parameters linked to climate and human factors. • Both local and global stability of the disease-free equilibrium are analyzed. • Sensitive analysis reveals a decisive role of temperature in dengue spread. • Sensitive analysis discloses a local role of precipitation and human population. • Climate changes aggregate dengue burden more than human population. Dengue fever (DF) is a re-emerging disease spread by mosquitoes. It is primarily found in the tropics and subtropics, and its prevalence is heavily influenced by global warming. A comprehensive understanding of how the changes in climate and human population affect future dengue epidemics is crucial for effective prevention and control. In this paper we extend a mechanistic compartmental model for mosquito dynamics of immature and mature stages, coupled with human population dynamics. Stability analysis of the disease-free equilibrium is carried out analytically, and the basic reproduction number is derived. Model parameters are explicitly linked to climatic variables and human population density. Model validation suggests that the basic reproduction number acts as a reliable measure of the spread ability of DF in response to future scenarios of climate and human population change. Our model predicts that the risk area of DF will expand considerably in mainland China, and the expansion fronts are mainly extended in the center and east. Most importantly, sensitivity analysis and model prediction both show that while temperature is critical in determining the threshold suitability for DF transmission, precipitation and human population density act locally to regulate the spreading DF patterns, where high values of these two factors may significantly accelerate the spreading process. Our results indicate a strong call for increased attention in the areas that are currently safe from DF, but climatically suitable for DF spread as consequence of the fast-economic growth and rapid urbanization. [ABSTRACT FROM AUTHOR]

• Two original multiseasonal models for a maize pest are developed. • Crop residues are burnt in one model (Slash-and-Burn Model), and buried in the soil in the other (Burying Model). • Stability analysis and R0 computation of semi-discrete models with 2D switchings. • Identification of thresholds of larvae destruction to reduce pest infestation. • Residue management strategies are discussed. Maize, also known as corn, is one of the most popular food in the world. Managing its Lepidoptera pests is a big deal as the larvae, which cause severe damages, develop inside maize stalks and ears. The most popular means of controlling insect pests remain chemical, but agricultural practices as the management of crop residues have been proven efficient. In this paper, we analyze the effect of the Maize Stalk Borer (MSB) Busseola fusca on maize crops and the efficiency of residue management over several cropping seasons. More precisely, we build two multi-seasonal mathematical models for the dynamics of MSB interacting with maize tissues. The models account for two types of residue management: either plant residues are burned after harvest or, are buried in the soil at the end of the cropping season to reduce pest reservoir for the following cropping seasons. A qualitative analysis of the models is carried out including the computation of a pest-free solution. Moreover, for each model, we compute the ecological threshold, also known as the basic reproduction number, that shapes the stability of the pest-free solution. To characterize the impact of parameter variations on the state variables of the models, we carry out a sensitivity analysis. The sensitivity analysis points out the leading role of the plant infestation rate and the senescence rate of crop residues on model outputs. In addition, numerical simulations are presented to illustrate our theoretical results and support the discussion. Notably, we found that the basic reproduction numbers have a linear relationship with the proportion of immature pests destroyed at the end of cropping seasons. Therefore, advocating management policies that lead to an increase in the proportion of immature pests destroyed at the end of cropping seasons could be helpful to control the dynamics of MSB. [ABSTRACT FROM AUTHOR]

Under the background that asymptomatic virus carriers are contagious and the virus in the infected individuals has mild pathogenicity and enhanced transmissivity for an infectious disease, the phenomenon appears that the majority of infected people do not show any symptoms, but can infect others. Multiple population-wide testing can screen out asymptomatic virus carriers in time. Thus, we develop an infectious disease transmission dynamics model that includes three stages: non-testing period, testing period and testing interval, with multiple population-wide testing and social distancing to study the effects of the first testing time, total testing number, and testing interval time on the transmission of infectious diseases in this paper. The existence, uniqueness, boundedness and positivity of the solution, as well as the formulas of the basic reproduction number and the control reproduction number of the established model are established The numerical results show that the earlier the population-wide testing measure is implemented, the fewer the final size and necessary testing frequency. In the initial stage of the larger-scale spread of infectious disease, the existing virus carriers are not the most. But if population-wide testing measure is implemented during this period, the strongest testing force is required to contain the spread of the epidemic. Besides, population-wide testing combined with restrictive social distancing will significantly reduce the final size, necessary testing frequency, and duration of the epidemic. The testing interval time should be no longer than the incubation period of the virus to prevent and control the epidemic accurately. Therefore, the paper provides a theoretic basis for developing and implementing scientific testing strategies. • A three-stage SEIR model with the multiple population-wide testing is proposed. • Minimum of testing is related to the start time of the first test and test interval. • The choice of test interval should no longer than the incubation period of the virus. • In this case, no obvious difference in the minimum of test and the final size appear. [ABSTRACT FROM AUTHOR]

The present paper aims to provide a supplementary result on a foot-and-mouth disease model proposed in Sun et al. (2022). We show that the endemic equilibrium for the model is globally attractive when the basic reproduction number is greater than one, which is an unsolved problem in the previously mentioned paper. [ABSTRACT FROM AUTHOR]

In this paper, a new mathematical model involving the general form of Caputo fractional derivative is studied for a real case of cholera outbreak. Fundamental properties of the new model including the equilibrium points as well as the basic reproduction number are explored. Also, an efficient approximation scheme on the basis of product-integration rule is established to solve the new model. Several kernel functions for the general fractional derivative are tested, and the results are compared with the real data of a cholera outbreak in Yemen. As a consequence, we find a special case in which the aforesaid outbreak is described better, for the corresponding numerical simulations are closer to the real data than the other classical and fractional frameworks. Next, we apply the most realistic model to investigate the effect of vaccination on the considered cholera outbreak. Simulation results show that earlier vaccination could reduce the number of infected individuals effectively, so mortality would have been reduced considerably if the vaccination had been performed earlier. [ABSTRACT FROM AUTHOR]

• This study will introduce a malaria model and formulate its corresponding Continuoustime Markov chain (CTMC). • The number of infected vector and infected host populations of vector-borne diseases depends on seasonal variability. • The threshold quantity R 0 is not same for the deterministic and periodic environments. • Seasonal variation influences the probability of disease outbreaks. • Random fluctuations in malaria modeling depend primarily on factors such as variations in mosquito biting rates, human mobility, and the efficacy of control interventions. • These stochastic elements introduce uncertainty into disease transmission dynamics and affect the accuracy of predictions and intervention planning. The best strategy for successfully controlling malaria transmission is suggested. • The analysis play the important role to understand the impact of various parameters and their stochastic behavior in the malaria model to prevent malaria outbreaks. Background: Malaria is the world's most fatal and challenging parasitic disease, caused by the Plasmodium parasite, which is transmitted to humans by the bites of infected female mosquitoes. Bangladesh is the most vulnerable region to spread malaria because of its geographic position. In this paper, we have considered the dynamics of vector-host models and observed the stochastic behavior. This study elaborates on the seasonal variability and calculates the probability of disease outbreaks. Methods: We present a model for malaria disease transmission and develop its corresponding continuous-time Markov chain (CTMC) representation. The proposed vector-host models illustrate the malaria transmission model along with sensitivity analysis. The deterministic model with CTMC curves is depicted to show the randomness in real scenarios. Sequentially, we expand these studies to a time-varying stochastic vector-host model that incorporates seasonal variability. Phase plane analysis is conducted to explore the characteristics of the disease, examine interactions among various compartments, and evaluate the impact of key parameters. The branching process approximation is developed for the corresponding vector-host model to calculate the probability outbreak. Numerous numerical results are accomplished to observe the analytical investigation. Results: Seasonality and contact patterns affect the dynamics of disease outbreaks. The numerical illustration provides that the probability of a disease outbreak depends on the infected host or vector. Additionally, periodic transmission rates have a great influence on the probability outbreak. The basic reproduction number (R 0) is derived, which is the main justification for studying the dynamical behavior of epidemic models. Conclusions: Seasonal variability significantly impacts malaria transmission, and the probability of disease outbreaks is influenced by time and the initial number of infected individuals. Moreover, the branching process approximation is applicable when the population size is large enough and the basic reproduction number is less than 1. In the future, such analysis can help decision-makers understand the impact of various parameters and their stochastic behavior in the vector-host model to prevent such types of disease outbreaks. [ABSTRACT FROM AUTHOR]

In this paper, a spatially heterogeneous SIRI epidemic model with general morbidity is studied, which conforms to the Fokker–Planck type diffusion law. The basic reproduction number R 0 of the model is introduced, and the threshold dynamics based on R 0 is discussed. In particular, with the help of elliptic eigenvalue theory, we determine the asymptotic profiles of the endemic equilibrium when the diffusion rate of susceptible individuals approaches zero or infinity. [ABSTRACT FROM AUTHOR]

In this paper, we consider an epidemic model in well-mixed multiplex networks with distributed time delay. Specifically, the model consists of two layers of well-mixed networks in the physical and virtual worlds, respectively, where two diffusive processes interact and influence each other within the same individual. We assume that there is a distributed time delay for an individual to become infected, but no delay for an individual to transition from unawareness to awareness. Our main results are as follows: Let R 0 P and R 0 V represent the basic reproduction numbers in the physical and virtual worlds, respectively. First, we demonstrate that the disease will die out for any delay time, provided that R 0 P ≤ 1 or 1 < R 0 P ≤ R 0 V. The latter condition emphasizes the significance of effective information spreading in eradicating the disease. Secondly, in the case of R 0 P > max ⁡ { 1 , R 0 V } , we establish that the model exhibits an endemic and information saturated equilibrium, denoted as E 3. Additionally, we show that the model is uniformly persistent, indicating the sustained outbreak of the disease. • We explore an epidemic model influenced by human awareness within the framework of a multiplex network. • The latent period of the infectious disease is concerned. • The necessary and sufficient conditions for the uniform persistence of disease are derived. • Our results highlight the crucial role of information spreading in disease eradication. [ABSTRACT FROM AUTHOR]

With the development of communications and transportation worldwide, the challenge of controlling epidemiological diseases becomes higher. The COVID19 has put all nations in a lethal confront with a severe disease that needed serious and painful actions. The sooner the actions, the less destructive the impact. In this paper, we incorporate what we believe is crucial but applicable to control the spread of COVID19 in the populations, that is, quarantine. We keep the model as simple as SI Kermack-McKendrick model with an additional compartment of quarantined patients. We established the system's basic properties and studied the stability of the disease-free equilibrium and its relation to the basic reproduction number R 0 in which we calculated its formula. The focus of our study is to measure the effect of quarantine rate on controlling the spread of COVID19. We use the data collected from the Ministry of Health in Saudi Arabia. We studied three different values of the quarantine rate where newly infectious patients are detected and isolated within 14, 7, and 5 days. The simulations show a significant effect of the quarantine where COVID19 can be fully controlled if the newly infected patient enters the quarantine within five days. These results were proposed to the Public Health Authority in Saudi Arabia and approved by the Ministry of Health in which they applied promptly. [ABSTRACT FROM AUTHOR]

The newest infection is a novel coronavirus named COVID-19, that initially appeared in December 2019, in Wuhan, China, and is still challenging to control. The main focus of this paper is to investigate a novel fractional-order mathematical model that explains the behavior of COVID-19 in Ethiopia. Within the proposed model, the entire population is divided into nine groups, each with its own set of parameters and initial values. A nonlinear system of fractional differential equations for the model is represented using Caputo fractional derivative. Legendre spectral collocation method is used to convert this system into an algebraic system of equations. An inexact Newton iterative method is used to solve the model system. The effective reproduction number (R 0) is computed by the next-generation matrix approach. Positivity and boundedness, as well as the existence and uniqueness of solution, are all investigated. Both endemic and disease-free equilibrium points, as well as their stability, are carefully studied. We calculated the parameters and starting conditions (ICs) provided for our model using data from the Ethiopian Public Health Institute (EPHI) and the Ethiopian Ministry of Health from 22 June 2020 to 28 February 2021. The model parameters are determined using least squares curve fitting and MATLAB R2020a is used to run numerical results. The basic reproduction number is R 0 = 1.4575. For this value, disease free equilibrium point is asymptotically unstable and endemic equilibrium point is asymptotically stable, both locally and globally. [ABSTRACT FROM AUTHOR]