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

A deterministic compartment model for the transmission dynamics of onchocerciasis with nonlinear incidence functions in two interacting populations is studied. The model is quantitatively analyzed to investigate it's 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 basic reproduction number is less than the unity. When the reproduction number is greater than the unity, we prove the existence of a locally asymptotically stable endemic equilibrium. Furthermore, bifurcation analysis was done by investigating the possibility of the co-existence of the equilibria of the model at R0<0 but near R0=0 by Center Manifold Theory.