A mathematical analysis of Zika virus transmission with optimal control strategies

This paper presents a mathematical model for transmission dynamics of Zika virus by considering standard incidence type interaction for the human to human transmission. The model involves the transmission through the bite of infected Aedes mosquitoes and human to human sexual transmission. The equilibria of the proposed model are found and the basic reproduction number R-0 is computed. If R-0 < 1, the disease-free equilibrium point is locally asymptotically stable and it is also globally asymptotically stable under certain conditions. The analysis shows that the model exhibits the occurrence of backward bifurcation, which suggests that when R-0 < 1 is not completely sufficient for eradicating the disease where the stable disease-free equilibrium co-exists with a stable endemic equilibrium. The endemic equilibrium point of the system exists and locally asymptotically stable under some restriction on parameters, whenever R-0 > 1. The sensitivity analysis is performed to identify the key parameters that affect the basic reproduction number, which can be regulated to control the transmission dynamics of the Zika. Further, this model is extended to the optimal control model and to reveals the optimal control strategies we used the Pontryagin's Maximum Principle. It has been noticed that the optimal control gives better result than without the optimal control model. Numerical simulation is presented to support our mathematical findings.