(2018). Modelling and Optimal Control of Lymphatics Filariasis disease

Abstract

We propose and analyze a compartmental nonlinear deterministic mathematical model for the Lymphatics Filariasis disease and optimal control strategies. The model is studied qualitatively using stability theory of differential equations and the basic reproduction number that represents the endemic indicator is obtained from the largest eigenvalue of the next-generational matrix. The local and global asymptotic stability conditions for disease-free equilibrium are determined and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies. Numerical results for the Lymphatics Filariasis dynamics and its optimal control revealed that a combination of preventions through the use of bed-net and annual mass treatment is the best strategy to eradicate the disease.