An epidemic model with optimal control strategies was investigated for Hepatitus C Viral disease that can be transmitted through infected individuals. In this study, we used a deterministic compartmental model for assessing the effect of different optimal control strategies for controlling the spread of Hepatitus C disease in the community. Stability theory of differential equations is us...

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...

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 < ...

Abstract. In this paper, a predator-prey-disease model with immune response in the infected prey is formulated. The basic reproduction number of the within-host model is defined and it is found that there are three equilibria: extinction equilibrium, infection-free equilibrium and infection-persistent equilibrium. The stabilities of these equilibria are completely determined by the reproduction...

Spatial heterogeneity, habitat connectivity, and rates of movement can have large impacts on the persistence and extinction of infectious diseases. These factors are shown to determine the asymptotic profile of the steady states in a frequency-dependent SIS (susceptible-infectedsusceptible) epidemic model with n patches in which susceptible and infected individuals can both move between patches...

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 ...

This paper considers the problem of constructing appropriate Lyapunov function for establishing global stability a disease-free equilibrium in epidemiological models. A generalised algorithm is proposed and it tested some selected Experience from application on test examples shows that easy to use, less cumbersome, yielded desired result, particularly models with homogeneous population. Thus, p...

A mathematical model of a within-host viral infection is presented. A local stability analysis of the model is conducted in two ways. At first, the basic reproduction number of the system is calculated. It is shown that when the reproduction number falls below unity, the disease free equilibrium (DFE) is globally asymptotically stable, and when it exceeds unity, the DFE is unstable and there ex...

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....

We present a deterministic mathematical model for malaria transmission with waning immunity. The model consists of five non-linear system of differential equations. We used next generation matrix to derive the basic reproduction number R0. The disease free equilibrium was computed and its local stability has been shown by the virtue of the Jacobean matrix. Moreover, using Lyapunov function theo...