The dynamics of the Zika with optimal Control strategies

Abstract

We proposed a mathematical model on Zika virus and presented its global dynamics with optimal control strategies. The basic model formulation and its mathematical results are presented. The proposed Zika model is locally asymptotically stable whenever the basic reproduction number ð“¡0<1 (disease free case) and ð“¡0>1 (endemic case). We show mathematical results for the global stability of the Zika model. The Zika model is globally asymptotically stable for the case of disease free when ð“¡0<1 and whenever ð“¡0>1, the model is globally asymptotically stable at the endemic state. We present an optimal control model for the dynamics of Zika virus with three controls, (the minimization of contacts among humans and mosquitoes by wearing long sleeve shirts, big trousers, stay in places with screen window to keep the mosquito outside, sleep under bed net),   (the contacts from mosquitoes to humans individuals by increasing the auto immunity), (increasing the death rate of mosquitos by using the insecticide spraying). The numerical simulation is performed for both the systems and the corresponding results are presented in graphical shape with different strategies. Finally, the brief conclusion is presented with source of references.