Studying the Effect of Parasite Switching in Optimal Control Analysis of Sleeping Sickness

Abstract

We construct and analyze an immunological mathematical model to explore within-host dynamics of a neglected tropical vector disease called Human African Trypanosomiasis (HAT). The disease, caused by a parasite with immune-evading strategies, is represented by six differential equations encompassing type 1 and type 2 parasites, naive macrophages, classical macrophages, alternative activated macrophages, and cytokines. Initial analysis without control measures reveals a disease-free equilibrium and two endemic equilibria, one with co-existing type 1 and type 2 parasites and the other with only one parasite type. Additionally, we explore the impact of control measures on parasite persistence and extinction. Two optimal control models assess the effect of two therapeutic drugs; one focuses on the parasite's invasion, and the other targets the parasite growth rate. Findings indicate that the first drug shifts the system from co-existence to a type 2 parasite endemic state, while the growth inhibitor drug eliminates the parasite from the host.