Stability and Hopf bifurcation analysis of an age-structured SVIRS epidemic model with temporary immunity

TL;DR

This paper analyzes an age-structured SVIRS epidemic model with temporary immunity, establishing stability conditions, bifurcation behavior, and numerical verification to understand disease dynamics.

Contribution

It introduces a novel age-structured SVIRS model with temporary immunity and provides a rigorous stability and bifurcation analysis.

Findings

Temporary immunity influences endemic stability

Hopf bifurcation occurs near endemic equilibrium

Numerical simulations confirm analytical results

Abstract

In this paper, we investigate an SVIRS epidemic model that incorporates both temporary immunity and an age-structured recovery process. By reformulating the system as a non-densely defined abstract Cauchy problem, we establish the existence and uniqueness of solutions and derive the basic reproduction number $ \mathcal{R}_0 $. The stability of the equilibria is analyzed through the associated characteristic equations, and the occurrence of Hopf bifurcation near the endemic equilibrium is rigorously demonstrated. Our theoretical results reveal that temporary immunity plays a crucial role in shaping the stability of the endemic state. Finally, numerical simulations are carried out to verify and illustrate the analytical findings.