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

Abstract

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 [Formula: see text] using the next generation matrix method. Also, we obtain the onchocerciasis-free and onchocerciasis endemic equilibrium solutions and show that if [Formula: see text] 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 [Formula: see text] 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.