In this work, we extend the mathematical model of leptospirosis disease by taking into account the exposed individuals, the related death rate and the transmission coefficients between susceptible human and infected vector. Initially, we present the local asymptotical stability of both the disease-free and endemic equilibrium. We use the Lyapunov function theory with some sufficient conditions....

An SIRS epidemic model incorporating media coverage with time delay is proposed. The positivity and boundedness are studied firstly. The locally asymptotical stability of the disease-free equilibrium and endemic equilibrium is studied in succession. And then, the conditions on which periodic orbits bifurcate are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf...

In this paper, a five–dimensional mathematical model is proposed for the transmission dynamics of HIV/AIDS within a population of varying size. In writing the model, we have divided the population under consideration into five sub classes of susceptible, infective, pre-AIDS, AIDS related complex and that of AIDS patients. The model has two non- negative equilibria namely, a disease free and the...

in this paper, a five–dimensional mathematical model is proposed for the transmission dynamics of hiv/aids within a population of varying size. in writing the model, we have divided the population under consideration into five sub classes of susceptible, infective, pre-aids, aids related complex and that of aids patients. the model has two non- negative equilibria namely, a disease free and the...

We consider the global dynamics of a virus propagation model in which infective cells pass through several successive stages, assuming that the incidence of infection and the removal rate of the virus are nonlinear functions given in an abstract, unspecified form. Suitable Lyapunov functionals are constructed to establish the existence of a threshold parameter, the basic reproduction number R0 ...

This paper considers a non-linear mathematical model for HIV epidemic that spreads in a variable size population through both horizontal and vertical transmission. The equilibrium points of the model system are found and their stability is investigated. The model exhibits two equilibria namely, the disease-free and the endemic equilibrium. It is found that if the basic reproduction number R0 < ...

The cure effect of a virus model with both cell-to-cell transmission and cell-to-virus transmission is studied. By the method of next generation matrix, the basic reproduction number is obtained. The locally asymptotic stability of the virus-free equilibrium and the endemic equilibrium is considered by investigating the characteristic equation of the model. The globally asymptotic stability of ...

We consider a mathematical model of epidemic spread  in which the  population  is partitioned  into five compartments of susceptible S(t), Infected I(t), Removed R(t), Prevented U(t) and the Controlled W(t). We assume each of the compartments comprises of cohorts of individuals which are  identical with respect to the disease status. We derive five systems of equations to represent each of the ...

To understand the impact of spatial heterogeneity of environment and movement of individuals on the persistence and extinction of a disease, a spatial SIS reaction-diffusion model is studied, with the focus on the existence, uniqueness and particularly the asymptotic profile of the steadystates. First, the basic reproduction number R0 is defined for this SIS PDE model. It is shown that if R0 < ...

In this paper, a delayed SIR model with exponential demographic structure and the saturated incidence rate is formulated. The stability of the equilibria is analyzed with delay: the endemic equilibrium is locally stable without delay; and the endemic equilibrium is stable if the delay is under some condition. Moreover the dynamical behaviors from stability to instability will change with an app...