Global Stability Analysis of Onchocerciasis Transmission Dynamics with Vigilant Compartment in Two Interacting Populations

Abstract

A deterministic compartmental model for the transmission dynamics of onchocerciasis with vigilant compartment in two interacting populations is studied. The model is qualitatively analyzed to investigate its global asymptotic behavior with respect to disease-free and endemic equilibria. It is shown, using a linear Lyapunov function, that the disease-free equilibrium is globally asymptotically stable when the associated basic reproduction number, R₀<1. When the basic reproduction number R₀>1, under some certain conditions on the model parameters, we prove that the endemic equilibrium is globally asymptotically stable with the aid of a suitable nonlinear Lyapunov function.