Hopf Bifurcation for an SIS model with age structure

TL;DR

This paper analyzes an SIS epidemic model with infection-age structure, demonstrating the existence of bifurcating periodic solutions through Hopf bifurcation theory, supported by explicit formulas and numerical simulations.

Contribution

It introduces a novel SIS model with age structure formulated as a non-dense Cauchy problem and applies advanced bifurcation theory to analyze its dynamics.

Findings

Existence of non-trivial periodic solutions bifurcating from equilibrium.

Explicit formulas for bifurcation direction and stability.

Numerical simulations confirm theoretical predictions.

Abstract

An SIS model is investigated in which the infective individuals are assumed to have an infection-age structure. The model is formulated as an abstract non-densely defined Cauchy problem. We study some dynamical properties of the model by using the theory of integrated semigroup, the Hopf bifurcation theory and the normal form theory for semilinear equations with non-dense domain. Qualitative analysis indicates that there exist some parameter values such that this SIS model has a non-trivial periodic solution which bifurcates from the positive equilibrium. Furthermore, the explicit formulae are given to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions. Numerical simulations are also carried out to support our theoretical results.