Mathematical modeling of Zika virus

Abstract

Zika virus (ZIKV) mathematical model is formulated. Optimal control strategies are introduced into the model. The basic properties of the model without control strategies are determined including the reproduction number. Pontryagin’s maximum principle is used to characterize the necessary conditions for optimal control of ZIKV. The preventive and treatment strategy without spraying the mosquitoes showed a great reduction in infected humans, however no significant reduction in the infected mosquitoes population. The use of preventive and insecticide techniques to minimize the spread of the virus showed a greater significance in the reduction of both infected humans and mosquitoes. The application of preventive, treatment and insecticide showed the best way of reducing the spread of ZIKV. The best strategy to minimize the spread of ZIKV is to use prevention, treatment and insecticide as control strategy at the same time.