Dynamics of epidemic models with asymptomatic infection and seasonal succession

TL;DR

This paper analyzes a seasonal epidemic model with asymptomatic infections, establishing conditions for disease persistence or eradication, and providing insights into how asymptomatic carriers and seasonal factors influence epidemic dynamics.

Contribution

It introduces a novel SIRS epidemic model incorporating asymptomatic infection and seasonal effects, with explicit analysis of stability and threshold conditions.

Findings

The basic reproduction number $\\mathcal{R}_0$ determines disease persistence or eradication.

The disease-free equilibrium is globally stable if $\mathcal{R}_0 \le 1$.

An endemic equilibrium exists and is globally stable when $\mathcal{R}_0 > 1$ and recovery rates are close.

Abstract

In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and valuated directly for this model, and the uniformly persistent of the disease and threshold dynamics are obtained. Specially, global dynamics of the model without seasonal force are studied. It is shown that the model has only a disease-free equilibrium which is globally stable if $\mathcal{R}_0\le 1$, and as $\mathcal{R}_0>1$ the disease-free equilibrium is unstable and the model has an endemic equilibrium, which is globally stable if the recovering rates of asymptomatic infective and symptomatic infective are close. These theoretical results provide an intuitive basis for understanding that the asymptomatic infective individuals and the disease seasonal transmission promote the evolution of epidemic, which allow us to predict the outcomes of control strategies during the course of the epidemic.