Optimal Control Problem for Cholera Epidemiology

Victor O. L. Anyuo; Nelson Owuor Onyango; Josephine Kagunda

Victor O. L. Anyuo School of Mathematics, University of Nairobi
Nelson Owuor Onyango School of Mathematics, University of Nairobi
Josephine Kagunda School of Mathematics, University of Nairobi

Keywords: SIR Epidemic Models, Singular Optimal Control, Basic Reproductive Number, Local Stability Analysis, Disease Free Equilibrium

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