The optimal strategy of wolbachia-infected mosquitoes release program: An application of control theory in controlling dengue disease

In this paper we discuss an application of control theory in a bio-system. We develop a mathematical model of dengue transmission in human and mosquito populations. We assume that the growth of human population is governed by a logistic equation. Two interventions are then introduced to control the disease, i.e. human vaccination and wolbachia-infected mosquitoes discharging into the wild mosquitoes population. We study the basic reproduction number for the system and also present the optimal control for the interventions via the Pontryagin Maximum Principle. Some numerical examples are explored, and the result indicates that the effect of the optimal control into the reduction of infected human population is critically influenced by both epidemiological parameters, such as the level of the contagiousness of the wolbachia infection, and economics factors, such as the cost of the implementation of the intervention program.