An optimal control problem for dengue transmission model with Wolbachia and vaccination

The release of Wolbachia-infected mosquitoes into the wild mosquitoes population is an excellent biological control strategy which can be effective against mosquito-borne infections. In this work, we propose a dengue transmission model that incorporates releasing Wolbachia into the wild mosquito population and vaccinating human population. We analyze the basic reproduction number, the existence and stability of the equilibria, and carry out the sensitivity analysis to quantify the effects of parameters on the basic reproduction number. The analysis shows that the basic reproduction number determines the stability of two equilibria, and two transmission probabilities are positively correlated with the basic reproduction number, especially, the transmission probability of human being infected byWolbachia-infected mosquitoes is more sensitive than that of wild mosquitoes. Based on an integrated control strategy for the prevention of dengue fever (vaccination, using mosquito nets, improved treatment of dengue and spraying insecticides), we derive the necessary conditions for the optimal control problem using Pontryagin’s Maximum Principle and carry out numerical simulations by MATLAB. Finally, the cost-effectiveness analysis of several control strategies is examined to determine the most feasible strategy. It shows that the most cost-effective integrated strategy is vaccination, using mosquito nets and spraying insecticides.