Modeling assumptions, optimal control strategies and mitigation through vaccination to Zika virus

Zika virus is amongst the deadly viruses still prevalent in more than 50 countries around the world. It is amosquitoes-borne disease that spread at fast rate in 2016. Zika virus belongs to the family of Flaviviridae virus. In this paper, a deterministic mathematical model is formulated to investigate the effects of vaccination in controlling the disease through optimal solution. The qualitative behavior of the proposed model is studied by using the theory of stability analysis. A basic reproduction number is computed by using Next Generation Technique todecide a threshold values of R 0 i.e. if R 0 < 1 ,the system is locally asymptotically stable and disease dies out and if R 0 > 1 dynamicsthe system is locally asymptotically unstable and diseases persist in the system. The global stability is also investigated via Lyapunov function. Numerical results were performed to see the effects of vaccination on the dynamics of the model with and without optimal interventions. The analysis of model suggests various strategies which help in the elimination of the disease.