Free Terminal Time in Optimal Control approach of Chikungunya Model

Abstract

Optimal control problems are an important mathematic tool used to reduce infectious diseases, most of works in this area considered time constant. In this paper, we present a free terminal optimal time control of Chikungunya epidemic model, which is an arthropod-borne virus (arbovirus) transmitted by mosquitoes of Aedes genus, with the order to give a minimum duration needed to reduce the infected group of both human and vector. We present a control simulating program using Matlab routines. The optimal control and the optimal final time are found using Pontryagin’s maximum principle and the additional transversality condition for the terminal time. We solved the optimality system by an iterative method, then we confirm the performance of the optimization strategy by numerical simulations. General Terms Optimal conrol, epidemiology, numerical analysis