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

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(Rhb)is obtained and it is shown that if Rhb<1,the onchocerciasis-free equilibrium is locally and globally asymptotically stable.Also,if Rhb>1,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 Rhb 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.

Transmission dynamics of onchocerciasis with two classes of infection and saturated treatment function

A mathematical model describing the epidemic interactions between humans and blackflies in the transmission of onchocerciasis is considered.In this model,the onchocerciasis infected human individuals are divided into two classes of infected humans with high and low microfilarial output incorporating saturated treatment function,which caters for high saturation of onchocerciasis disease.We analyze the model feasible region and obtain the basic reproduction number(R_(hb))using the next generation matrix method.Also,we obtain the onchocerciasis-free and onchocerciasis endemic equilibrium solutions and show that if R_(hb) is less than unity,the onchocerciasis-free equilibrium is locally and globally asymptotically stable.Furthermore,we employed a Lyapunov function to analyze the global asymptotic stability of the onchocerciasis—endemic equilibrium whenever Rhb is greater than unity.In addition,data on mass drug distribution of ivermectin drug to combat onchocerciasis prevalence in Ekiti state of Nigeria were fitted to the model.Graphical results reveal that consistent annual or bi-annual distribution of ivermectin drug in the region is effective in reducing the disease menace.Further simulations also show that public health control measures are needed to minimize infectious contact between humans and blackflies which leads to onchocerciasis infections and visual blindness.