Global stability in an age-structured SIRS malaria transmission 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 $R_0>1$.