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

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