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.