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.