A mathematical model of Zika virus transmission with saturated incidence and optimal control: A case study of 2016 zika outbreak in Puerto Rico.

Zika virus outbreak is creating a global public health hazard due to its increasing prevalence rate and neurological complication in affected individuals. In this work we have developed and studied an ODE compartmental Zika model with non-linear saturated incidence function and three control measures including prevention control from vector bite, treatment control of infected host and vector killing control. Our theoretical analysis shows that the disease free equilibrium is locally as well as globally asymptotically stable when the basic reproduction number is less than unity. The virus is uniformly persistent when the basic reproduction number is greater than unity. An endemic equilibrium point exists and locally stable when the basic reproduction number is greater than unity. The model is validated by fitting the model to real reported data of 2016 Zika outbreak in Puerto Rico and estimated the model parameters. We also have studied the basic reproduction number and effective reproduction number of the outbreak. Sensitivity analysis has been carried out to find most sensitive parameters. The optimal control and efficiency analysis has been done to find the policy of control variables. Lastly, the manuscript is ended by some conclusions. [ABSTRACT FROM AUTHOR]