Mathematical modeling for the transmission potential of Zika virus with optimal control strategies

In this paper, we formulate a new Zika virus model in light of both mosquito and human transmission along with the human awareness in the host population. Initially, we assumed that the virus is transmitted to humans through a mosquito bite and then transmits to his or her sexual partner. Further, we investigated the mathematical results and stability analysis and proved that the model is asymptotically stable both locally and globally. We applied the Castillo-Chavez approach for establishing global stability. Similarly, we presented the existence of endemic equilibrium and demonstrate that the model is locally and globally asymptotically stable using a suitable Lyapunov function at endemic state, upon backward bifurcation analysis we proposed that no bifurcation exists for our model. The sensitivity analysis is carried out and verified that the probability per biting of the susceptible mosquito with the infected human is the most sensitive parameter. Furthermore, we developed a Zika control model and incorporated three controls. These controls are prevention through bed nets and mosquito repellents, treatment of Zika patients, and the spray of insecticides on mosquitoes. The graphical results of the model with control and without control are obtained through a numerical scheme. The infection caused by the Zika virus would be more efficiently eliminated using the new idea of human awareness and bilinear incidence presented in this paper.