Sharif Digital Repository

This paper is concerned with global analysis of a delay SVEIR epidemiological model in a population of varying size. By using Lyapunov stability method and LaSalle's invariance principle for delay systems, we prove that when there is no endemic equilibrium, the disease free equilibrium is globally asymptotically stable, otherwise the endemic equilibrium is globally stable  

An SIS epidemiological model in a population of varying size with two dissimilar groups of susceptible individuals has been analyzed. We prove that all the solutions tend to the equilibria of the system. Then we use the Poincaré Index theorem to determine the number of the rest points and their stability properties. It has been shown that bistability occurs for suitable values of the involved parameters. We use the perturbations of the pitchfork bifurcation points to give examples of all possible dynamics of the system. Some numerical examples of bistability and hysteresis behavior of the system has been also provided  

A deterministic model for human immunodeficiency virus (denoted HIV) infection in the presence of combination therapy is considered. Global asymptotic stability of the disease-free equilibrium is discussed and the endemic equilibrium is also investigated. © 2006 Elsevier Ltd. All rights reserved  

This paper is concerned with global analysis of an SIS epidemiological model in a population of varying size with two dissimilar groups of susceptible individuals. We prove that this system has no periodic solutions and use the Poincar index theorem to determine the number of rest points and their stability properties. It has been shown that multiple equilibria (bistability) occurs for suitable values of parameters. We also give some numerical examples of all possible bifurcations of this system  

This paper is concerned with global analysis of an SAIS epidemiological model in a population of varying size introduced by Busenberg and van den Driessche. In this model the population is divided into three subgroups of susceptible, asymptomatic and infective individuals. It has been shown that this system has no periodic solutions and all its trajectories tend to the equilibria of the system. We use the Poincaré Index theorem to determine the number of the equilibria and their stability properties. We have shown that bistability occurs for suitable values of parameters and found a set of examples of all possible dynamics of the system  

Recent progress in the areas of network science and control has shown a significant promise in understanding and analyzing epidemic processes. A well-known model to study epidemics processes used by both control and epidemiological research communities is the susceptible–infected–susceptible (SIS) dynamics to model the spread of disease/viruses over contact networks of infected and susceptible individuals. The SIS model has two metastable equilibria: one is called the endemic equilibrium and the other is known as the disease-free or healthy-state equilibrium. Control theory provides the tools to design control actions (allocating curing or vaccination resources) in order to achieve and...