A discrete-time epidemic SISI model

TL;DR

This paper introduces a discrete-time SISI epidemic model with constant population, analyzing its fixed points and long-term behavior through quadratic stochastic operators, providing insights into disease dynamics.

Contribution

It develops a novel discrete-time SISI epidemic model and proves the uniqueness of its interior fixed point, analyzing its stability and limit behavior.

Findings

Unique interior fixed point established

Conditions for limit behavior analyzed

Model provides new insights into epidemic dynamics

Abstract

We consider a discrete-time epidemic SISI model in case when the population size is a constant, so the per capita death rate is equal to per capita birth rate. The evolution operator of this model is a non-linear operator which depends on seven parameters. Reducing it to a quadratic stochastic operator, we prove uniqueness of interior fixed point of the operator and study the limit behavior of the trajectory under some conditions to parameters.