Analysis and optimal control of a deterministic Zika virus model

In this paper, we consider a deterministic model explaining how Zika virus is transmitted between human and mosquito. The human population is divided into three groups as susceptible \((x_1)\), infected \((x_2)\), and treated \((x_3)\). Similarly, the mosquito population is divided into susceptible \((y_1)\) and infected \((y_2)\) groups. First, we conduct the local and global stability of the disease-free and endemic equilibrium points in relation to the basic reproductive number. We also study the sensitivity of the basic reproductive number and the endemic equilibrium point with respect to each parameters used in the model. Furthermore, we apply optimal control theory to show that there are cost effective control methods with the prevention effort \((u_1)\) of the contact between human and vector and the effort of treatment \((u_2)\) for human. Finally, we provide numerical simulations to support and illustrate some of the theoretical results.