On the approximate solutions and asymptotic stability of an onchocerciasis transmission model

Abstract

This article describes the mathematical model derivation describing river blindness disease transmission in human and vector (blackflies) host population. The effect of incomplete resistance to re-infection in human individuals who recovered from the disease after treatment but are still subjected to repeated exposures to infected blackflies bite is investigated. Also, the basic reproduction number [Formula: see text] is obtained and it is shown that if [Formula: see text], the onchocerciasis-free equilibrium is locally and globally asymptotically stable. Also, if [Formula: see text], the onchocerciasis-endemic equilibrium is globally asymptotically stable. Moreover, the Differential Transform Method (DTM) and Runge–Kutta fourth-order method is employed via the computational software Maple 18 to solve and obtain the approximate solutions of the model system equations, which showed that the numerical results favorably compare with each other. Simulations reveal that increase in biting and transmission rates leads to an increase of [Formula: see text] and incomplete resistance to re-infection due to consistent exposure to blackflies bites. Also, simulations of the approximate solutions of the model state equations are provided.