Modelling and stability analysis of SVEIRS yellow fever two host model

Abstract

We describe transmission dynamics of yellow fever (YF) within two host populations, and build up a deterministic SVEIRS model with vaccination to the entire new born. The model aims at clarifying contributions of mathematical ideas in studying the impact of YF disease dynamics. We examine existence of equilibrium solutions and give out conditions that are sufficient for existence of realistic equilibria. Threshold of the form R₀ = √(R_hv + R_vm) is obtained, where R_hv and R_vm are reproduction numbers for human-vector and vector-primate compartments respectively. Stability analysis of the equilibria is presented; trace-determinant approach is used in determining local stability of DFE and Metzler matrix for global stability. Lyapunov function is used in establishing conditions for global stability of EE. Our results suggests that eradication of the infection to human population is possible only if R_hv < 1 and R_vm <1. Due to new births and immunity loss to YF after ten years, susceptible class will always be refilled and hence continuous vaccination is essential.