Dynamic analysis and optimal control of Zika virus transmission with immigration

In this paper, a type of Zika virus model with immigration is considered. Additionally based on the risk of infected immigrants, we propose a control measure of screening for immigrants and a three-measure control model of combined mosquito prevention and killing. The existence and stability of the equilibrium in the Zika virus model are analyzed. The necessary conditions for the existence of the optimal solution are given using Pontryagin's maximum principle. We focused on testing screening of the immigrating population to ensure a reduction in the transmission of the virus. Models have demonstrated that in combination with routine mosquito control measures and the appropriate use of mosquitoicides, the transmission of Zika virus in the population can be effectively reduced.