Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes

Abstract

We investigate the dynamical behaviors of a class of discrete SIRS epidemic models with nonlinear incidence rate and varying population sizes. The model is required to possess different death rates for the susceptible, infectious, recovered, and constant recruitment into the susceptible class, infectious class, and recovered class, respectively. By using the inductive method, the positivity and boundedness of all solutions are obtained. Furthermore, by constructing new discrete type Lyapunov functions, the sufficient and necessary conditions on the global asymptotic stability of the disease-free equilibrium and endemic equilibrium are established.

Population dynamics in educational institutions considering the student satisfaction

“…For c > 0, Eqs. (8)- (13) and (19) can be used for predicting the size of the D-population, which will always exist.…”

A Consistent Discrete Version of a Nonautonomous SIRVS Model

“…Most of the epidemiological models in the literature are continuous models. In spite of this, recently, there has been a growing interest in discrete-time models [8,29,31,32,21,12,13]. In this work, we will use Mickens nonstandard difference (NSFD) scheme to achieve a discretization of a family of continuous epidemiological models with vaccination and general incidence function considered in [27].…”