Optimal control of dengue vector based on a reaction-diffusion model?

In recent decades, the incidence rate of dengue fever has increased sharply in the world, which has caused a serious burden on society as a whole. Considering that using Wolbachia to inhibit the spread of dengue fever is an effective and sustainable mean, we try to explore the effect of the control measures by establishing a mathematical model. Due to the uneven distribution of mosquitoes in space, a reaction-diffusion model containing the wild mosquito population and the Wolbachia-infected mosquito population with control is established. Firstly, the dynamic behaviors of the uncontrolled model are analyzed. It is found that Wolbachia may completely invade the wild mosquito population or fail, which is mainly determined by the initial proportion of Wolbachia, and the diffusion has a negligible effect on the successful transmission of Wolbachia. Secondly, the optimal control strategies in the case of no diffusion and with diffusion are studied. The specific expression of optimal control is obtained. Thirdly, the results are verified and the influence of diffusion on the optimal control is discussed by numerical simulations. The results show that the implementation of control will cause Wolbachia to completely invade the wild mosquito population. The greater the control force, the shorter the time required for a complete invasion. The control force of diffusion system is much greater than that of non diffusion system. Finally, all the conclusions are showed and explained, and some discussions are given.(c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.