Modelling analysis of Zika virus with saturated incidence using optimal control theory

Abstract

A non-linear mathematical model of the Zika virus is proposed and analysed the impact of optimal control strategies with the saturated incident. The basic reproduction number (R0) is computed and performed sensitivity analysis to identify the key parameters that influence the basic reproduction number. To investigate the optimal control strategies, three types of time-dependent control parameters are introduced in the system to reduce the transmission. Electronic devices, insecticide-treated bed nets, and mosquito repulsive lotions are used to reduce mosquito biting rates. Keeping this fact, found some suitable optimal control strategies to eradicate the transmission of the disease in the tropical area. Pontryagin's maximum principle is used to manifest the optimal control strategies. It is noticed that the optimal control model gives a better result than the model without optimal control. Finally, the results of the optimal controls are compared by using numerical simulation.