SIR models with demography, random transmission coefficient and non-autonomous vaccination rate

TL;DR

This paper analyzes advanced SIR epidemic models with demography, stochastic transmission, and dynamic vaccination, providing conditions for disease eradication or endemicity, supported by theoretical proofs and numerical simulations.

Contribution

It introduces a comprehensive analysis of SIR models with random transmission and non-autonomous vaccination, establishing existence, uniqueness, and long-term behavior conditions.

Findings

Conditions for disease eradication identified

Models demonstrate endemic equilibrium under certain parameters

Numerical simulations validate theoretical results

Abstract

In this paper we investigate the asymptotic behavior of some SIR models incorporating demography, bounded random transmission coefficient and a time-dependent vaccination strategy targeting the susceptible population. In this setting, we establish the existence and uniqueness of non-negative global solution of the models and derive conditions under which either the disease is eradicated or becomes endemic. In addition, the theoretical results are further illustrated by several numerical simulations.