A stochastic differential equation approach for an SIS model with non-linear incidence rate

TL;DR

This paper develops a stochastic differential equation model for an SIS epidemic with a non-linear incidence rate, analyzing its stability, persistence, and extinction conditions, and validating findings through simulations.

Contribution

It introduces an analytically tractable SDE-based SIS model with non-linear incidence, providing new insights into its stability and long-term behavior.

Findings

Existence of positive solutions confirmed

Conditions for disease extinction and persistence established

Unique stationary measure identified under certain conditions

Abstract

In this paper, we study an analytically tractable SIS model with a non-linear incidence rate for the number of infectious individuals described through a stochastic differential equation (SDE). We guarantee the existence of a positive solution, and we study its regularity. We study the persistence and extinction regimes, and we give sufficient conditions under which the disease-free equilibrium point is an asymptotically stable equilibrium point with probability one. We provide sufficient conditions under which the model admits a unique stationary measure. Finally, we illustrate our findings using simulations.