Global stability in an age-structured SIRS malaria transmission model

TL;DR

This paper develops and analyzes an age-structured malaria transmission model, proving global stability of disease-free and endemic states based on the basic reproduction number, using advanced mathematical techniques.

Contribution

It introduces a novel age-structured SIRS model for malaria and provides rigorous mathematical proof of stability conditions, extending previous models.

Findings

Global stability of the parasite-free equilibrium when R0 ≤ 1

Numerical evidence of endemic equilibrium stability when R0 > 1

Exclusion of backward bifurcation in the model

Abstract

This paper proposes and analyzes a malaria transmission model structured by the chronological age of the human host population. The model couples an age-structured SIRS system for humans, incorporating waning immunity, with an SI system for mosquitoes under mass-action transmissions. Using integrated semigroup theory and spectral analysis, we establish the well-posedness of the model, derive the basic reproduction number, and prove the global asymptotic stability of the parasite-free equilibrium by using a Lyapunov functional, when $R_0\leq 1$, thereby excluding the possibility of backward bifurcation. Numerical simulations further suggest the global stability of the endemic equilibrium when $R_0>1$.