The Optimal Release Strategy of Wolbachia Infected Mosquitoes to Control Dengue Disease

Abstract

The paper discusses a mathematical model of dengue transmission. We assume that to control the spreading of the disease in human population we give vaccination to newborn human population and introduce wolbachia-infected mosquitoes into the wild mosquitoes population. The presence of wolbachia is assumed to be able to reduce the life expectancy of the mosquitoes and the biting rate due to the damage of their proboscis. The optimal control for the interventions are obtained 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 in?uenced by both epidemiological parameters, such as the level of the contagiousness of the wolbachia infection, as well as economics factors, such as the cost of the implementation of the intervention program. It also reveals that if wolbachia disease is dif?cult to transmit among the mosquitoes, introducing too many wolbachia-infected mosquitoes into the wild could be counter productive.