Optimal Control Problem for Cholera Epidemiology

Abstract

In this paper, the major objective was to theoretically investigate, proof the existence and local optimality state of singular control by applying L1 type objective function. The objective function L1 has been applied in a Compartmental model since it is linear in the control variables. Generalized Legendre-Clebsch Condition applied showed the existence of singular control for both vaccination and sanitation that are optimal. The condition for local stability of the model was also established and the basic reproductive number assimilated. The disease-free equilibrium of the model is locally asymptotically stable if 𝑅𝑂< 1, and unstable if 𝑅𝑂>1. This means that all interventions applied need to reduce the basic reproductive number to reduce the force of infection.