Mathematical analysis of a model for ectoparasite-borne diseases

A new deterministic model for ectoparasite-borne diseases (which comprises four nonlinear coupled differential equations) is designed and analyzed. A full stability analysis of thismodel is investigated. First, the basic reproduction numbers (R-1, R-2, and R-3) of the model are determined. The model has a locally and globally asymptotically stable disease-free equilibrium point when R-0 = max{R-1, R-2} <= 1. A unique infestation-only boundary equilibrium point is shown to be globally asymptotically stable whenever R-2 < 1 < R-1 by using a nonlinear Lyapunov function of Goh-Volterra type, in conjunction with the LaSalle's invariance principle. On the other hand, the model has a unique globally asymptotically stable infected-only boundary equilibrium point whenever R-1 < 1 < R-2. Moreover, the model has a unique endemic equilibrium point that is globally asymptotically stable provided that R-1 > R-2 > 1 and R-3 > 1. Finally, it is shown that replacing themass incidence function with the standard incidence function in the ectoparasite-borne diseases model with mass action incidence does not alter the qualitative dynamics of the model.