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In this paper, we consider a stochastic SIRS epidemic model with nonlinear incidence and Markovian switching. By using the stochastic calculus background, we establish that the stochastic threshold ℜswt can be used to determine the compartment dynamics of the stochastic system. Some examples and numerical simulations are presented to confirm the theoretical results established in this paper. [ABSTRACT FROM AUTHOR]

In this paper, an age structured epidemic Susceptible-Infected-Quarantined-Recovered-Infected (SIQRI) model is proposed, where we will focus on the role of individuals that leave the R-class before being completely recovered and thus will participate again to the disease transmission. We investigate the asymptotic behavior of solutions by studying the stability of both trivial and positive equilibria. In order to see the impact of the different model parameters like the relapse rate on the qualitative behavior of our system, we firstly, give an explicit expression of the basic reproduction number R0, which is a combination of the classical basic reproduction number for the SIQR model and some other model parameters, corresponding to the individuals infected by the relapsed ones. It will be shown that, if R0 ≤ 1, the disease free equilibrium is globally asymptotically stable and becomes unstable for R0 > 1. Secondly, while R0 > 1, a suitable Lyapunov functional is constructed to prove that the unique endemic equilibrium is globally asymptotically stable on some subset Ω0. [ABSTRACT FROM AUTHOR]

In this paper, we construct a model to describe the transmission of HIV in a homogeneous host population. By considering the specific mechanism of HIV, we derive a model structured in three successive stages: (i) primary infection, (ii) long phase of latency without symptoms, and (iii) AIDS. Each HIV stage is stratified by the duration for which individuals have been in the stage, leading to a continuous age-structure model. In the first part of the paper, we provide a global analysis of the model depending upon the basic reproduction number ℜ0. When ℜ0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable and the infection is cleared in the host population. On the contrary, if ℜ0 > 1, we prove the epidemic's persistence with the asymptotic stability of the endemic equilibrium. By performing the sensitivity analysis, we then determine the impact of control-related parameters on the outbreak severity. For the second part, the initial model is extended with intervention methods. By taking into account antiretroviral therapy (ART) interventions and the probability of treatment drop out, we discuss optimal intervention methods which minimize the number of AIDS cases. [ABSTRACT FROM AUTHOR]

In this paper we the study of dynamics of time since infection structured vector born model with the direct transmission. We use standard incidence term to model the new infections. We analyze the corresponding system of partial differential equation and obtain an explicit formula for the basic reproduction number ℜ0. The diseases-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than one, ℜ0 < 1. Endemic equilibrium exists and is locally asymptotically stable when ℜ0 > 1. The disease will persist at the endemic equilibrium whenever the basic reproduction number is greater than one. [ABSTRACT FROM AUTHOR]

This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability analysis of equilibria have been investigated. It has been shown that the disease free equilibrium point (DFE) is globally asymptotically stable if the basic reproduction number is less than unity and the transmission rate of infection less than some threshold. The system exhibits the transcritical bifurcation at DFE with respect to the cure rate. We have also found the condition for occurring the backward bifurcation, which implies the value of basic reproduction number less than unity is not enough to eradicate the disease. Stability or instability of different endemic equilibria has been shown analytically. The system also experiences the saddle-node and Hopf bifurcation. The existence of Bogdanov-Takens bifurcation (BT) of co-dimension 2 has been investigated which has also been shown through numerical simulations. Here we have used two control functions, one is vaccination control and other is treatment control. We have solved the optimal control problem both analytically and numerically. Finally, the efficiency analysis has been used to determine the best control strategy among vaccination and treatment. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate a fractional diffusive model for hepatitis B virus (HBV) infection with capsids and immune response presented by cytotoxic T lymphocyte (CTL) cells. We derive the conditions for global asymptotic stability of the steady states of the model in terms of the basic reproduction number R0 and the immune response reproduction number R1. By constructing appropriate Lyapunov functionals, it is shown that the infection-free equilibrium is globally asymptotically stable when R0 ≤ 1, the immune-free infection equilibrium is globally asymptotically stable when R1 ≤ 1 < R0 and the infection equilibrium with CTL immune response is globally asymptotically stable when R1 > 1. Numerical simulations are performed to illustrate the analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the immune response in a fractional order model for HIV dynamics, for distinct disease transmission rates and saturated cytotoxic T-lymphocyte (CTL) response. Our goal is twofold: (i) to analyze the role of the order of the fractional derivative, α, on the efficacy of the immune response, (ii) to examine the immune response for distinct transmission functions, in the presence of saturated CTL response. We compute the reproduction number of the model and state the stability of the disease-free equilibrium. We discuss the results of the model from an epidemiological point of view. [ABSTRACT FROM AUTHOR]

Ecoepidemiology is a well-developed branch of theoretical ecology, which explores interplay between the trophic interactions and the disease spread. In most ecoepidemiological models, however, the authors assume the predator to be a specialist, which consumes only a single prey species. In few existing papers, in which the predator was suggested to be a generalist, the alternative food supply was always considered to be constant. This is obviously a simplification of reality, since predators can often choose between a number of different prey. Consumption of these alternative prey can dramatically change their densities and strongly influence the model predictions. In this paper, we try to bridge the gap and explore a generic eco- epidemiological system with a generalist predator, where the densities of all prey are dynamical variables. The model consists of two prey species, one of which is subject to an infectious disease, and a predator, which consumes both prey species. We investigate two main scenarios of infection transmission mode: (i) the disease transmission rate is predator independent and (ii) the transmission rate is a function of predator density. For both scenarios we fulfil an extensive bifurcation analysis. We show that including a second dynamical prey in the system can drastically change the dynamics of the single prey case. In particular, the presence of a second prey impedes disease spread by decreasing the basic reproduction number and can result in a substantial drop of the disease prevalence. We demonstrate that with efficient consumption of the second prey species by the predator, the predator-dependent disease transmission can not destabilize interactions, as in the case with a specialist predator. Interestingly, even if the population of the second prey eventually vanishes and only one prey species finally remains, the system with two prey species may exhibit different properties to those of the single prey system. [ABSTRACT FROM AUTHOR]

Coffee leaf rust (CLR) is one of the main diseases that affect coffee plantations worldwide. It is caused by the fungus Hemileia vastatrix. Damages induce severe yield losses (up to 70%). Its control mainly relies on cultural practices and fungicides, the latter having harmful ecological impact and important cost. Our goal is to understand the propagation of this fungus in order to propose a biocontrol solution, based on a mycoparasite that inhibits H. vastatrix reproduction. We develop and explore a spatio-temporal model that describes CLR propagation in a coffee plantation during the rainy and dry seasons. We show the existence of a solution and prove that there exists two threshold parameters, the dry and rainy basic reproduction numbers, that determine the stability of the equilibria for the dry and rainy season subsystems. To illustrate these theoretical results, numerical simulations are performed, using a non-standard finite method to integrate the pest model. We also numerically investigate the biocontrol impact. We determine its efficiency threshold in order to ensure CLR eradication. [ABSTRACT FROM AUTHOR]

Visceral leishmaniasis in dogs is believed to have an impact on the prevalence of the disease in human populations. Here, we continue the analysis of the nested immuno-epidemiological model of visceral leishmaniasis in dogs, including a proof of well-posedness using functional analytical methods. Once well-posedness is established, we continue stability analysis of the endemic equilibria and provide necessary and sufficient conditions for the presence of backward bifurcation, and prove the instability of the lower endemic equilibrium in the presence of backward bifurcation. Lastly, we provide a number of simulations of the model using a number of control strategies. Control measures currently in use attempt to reduce the parasite load in the host, reduce the vector population, reduce the vector biting rate, and remove infected hosts. We examine various combinations of these strategies and conclude that a strategy combining culling infected dogs and removing vectors from the population by means such as insecticide will be the most effective. [ABSTRACT FROM AUTHOR]

A coupled pig-human Nipah virus disease model is studied in a commercial farm to understand dynamics of disease spillover from pig to human. To portray the specific scenario, two parameters representing biosecurity level and selective culling are included in the system. Along with standard equilibrium analysis, backward and Hopf bifurcation phenomena are demonstrated analytically and numerically. Optimal control of culling alone and also with other controls for the minimization of loss are discussed. It is observed that, irrespective of its application rate, culling is more effective in presence of other controls. Parameter sensitivity analysis of system solution has been used to identify significant parameters for the change of disease dynamics. Sensitivity test is also performed on the objective function of optimal control problem, which singled out crucial parameters influencing the economic loss of farm-owner. Based on this study, some strategies regarding application of various controls are suggested. [ABSTRACT FROM AUTHOR]

We study a competitive infection-age structured SI model between two diseases. The well-posedness of the system is handled by using integrated semigroups theory, while the existence and the stability of disease-free or endemic equilibria are ensured, depending on the basic reproduction number R0x R 0 x and R0y R 0 y of each strain. We then exhibit Lyapunov functionals to analyse the global stability and we prove that the disease-free equilibrium is globally asymptotically stable whenever max{R0x, R0y} ≤ 1 max { R 0 x , R 0 y } ≤ 1 . With respect to explicit basin of attraction, the competitive exclusion principle occurs in the case where R0x ≠ R0y R 0 x ≠ R 0 y and max{R0x, R0y} > 1 max { R 0 x , R 0 y } > 1 , meaning that the strain with the largest R0 persists and eliminates the other strain. In the limit case R0x = Ry0 > 1 R 0 x = R y 0 > 1 , an infinite number of endemic equilibria exists and constitute a globally attractive set. [ABSTRACT FROM AUTHOR]