Optimal Control Problem for Cholera Epidemiology

Abstract

Optimal control is vital in determining control policies for diseases that are infectious. A SIR-model with vaccination and sanitation is considered. The extant and local stability analysis of (DFE) disease-free equilibrium point is considered and its basic reproduction number (Ro) is derived. We also investigate the existence of singular control and its local optimality with an aim to nd an optimal combinations of sanitation and vaccination to minimize infectious individuals (force of infection), bacteria concentration and the costs associated with the strategies.Majority of the projects done on SIR- models dealt with the quadratic costs function in respect to control variables. In this thesis, we consider L1- type objective function that is linear in the control variables. We applied PMP in the characterization of the levels of optimal of the applied strategies that satisfy the necessary optimality conditions. From the computation it is shown that both the optimal controls can be singular. Keywords: SIR Epidemic Models, Singular Optimal Control, PMP, Basic reproduction number, disease-free equilibrium, local stability analysis, vaccination, sanitation.