Optimal OPTIMAL CONTROL ANALYSIS FOR A LYMPHATIC FILARIASIS MODEL

Abstract

In this paper, a mathematical model for the transmission dynamics of lymphatic filariasis is presented. Human and mosquito populations are divided based on their lymphatic filariasis status. The human population is subdivided into six (6) compartments, while the mosquito population is subdivided into three (3) compartments. The disease-free equilibrium (DFE) and the endemic equilibrium states are proven to be the model's two equilibrium states. In terms of the model's demographic and epidemiological characteristics, an explicit formula for the effective reproduction number was found. The disease-free equilibrium state was discovered to be locally asymptotically stable using the Routh-Hurwitz criterion if the basic reproduction number is less than one. By using Castillo-Chavez, the disease-free equilibrium state was found to be globally asymptotically stable. This means that lymphatic filariasis could be put under control in a population when the reproduction number is less than one. Sensitivity analysis was carried out on the basic reproduction number to ascertain the parameters that have an impact on the reproduction number The results show that some parameters that appeared in the reproduction number have an impact on the reproduction number.. An optimal control problem was formulated and analyzed using Pontryagin’s Maximum Principle to determine the optimality system. The system was solved numerically using the forward and backward sweep method and results show that the combination of treated bed nets, antibiotics, and indoor residual spray is the most effective way to prevent the spread of filariasis in a community.