An optimal control of hookworm transmissions model with differential infectivity

Abstract

In this study, we develop and analyze a mathematical model of hookworm transmission dynamics with two different classes of infection and different stages of parasite developments. We show that the model exhibits two equilibrium points, of which the disease free equilibrium (l0) is locally asymptotically stable when R0<1 and unstable if R0>1, and using Lyapunov function, the endemic equilibrium point is globally asymptotically stable whenever R0<1 and unstable if R0>1. We propose an optimal control strategy, where we consider three control functions u1(t), u2(t) and u3(t), with u1(t) as proper sanitation and personal hygiene on exposed class, u2(t) is considered as preventive measure(awareness) on moderate infection class and u3(t) as a chemotherapy treatments on heavy infection class. We analyze the effect of these three control functions on the model using a version of Pontryagin’s Maximum Principle to obtained the representations of the control functions. The analysis shows that when chemotherapy and awareness are applied on heavy and moderate infections, the effect of improvement of personal hygiene has less effect on the model.