Local Stability Analysis of Onchocerciasis Transmission Dynamics With Nonlinear Incidence Functions in Two Interacting Populations

Abstract

A deterministic compartmental model for the transmission dynamics of onchocerciasis with nonlinear incidence functions in two interacting populations is studied. The model is qualitatively analyzed to investigate its local asymptotic behavior with respect to disease-free and endemic equilibria. It is shown, using Routh-Hurwitz criteria, that the disease-free equilibrium is locally asymptotically stable when the associated basic reproduction number is less than the unity. When the basic reproduction number is greater than the unity, we prove the existence of a locally asymptotically stable endemic equilibrium.