An Optimal Integrated Vector Control for Prevention the Transmission of Dengue

Dengue is a tropical infectious disease caused by dengue virus which is transmitted by mosquitos such as Aedes Aegypti and Aedes Albopictus. The spread of this disease could be controlled by applying some optimal strategies. In this research, we study optimal strategy in controlling the spread of dengue by taking into consideration an integrated vector control strategy. The strategy combines chemical and non-chemical vector control methods to prevent the transmission of vector-borne disease. If we assume that the control functions are constant functions then numerically we obtain a critical chemical control which leads to the non-endemic condition. When the chemical and non-chemical controls are varying in time, we obtain the analytical form of the both control functions by using Pontryagin Maximum Principle. The numerical simulations are performed using the Steepest Descent method and the results show that the peak of the non-chemical control effect occurs at the end of the observation time. Conversely, the chemical control reaches the maximum effect at the early of the observation time. It indicates that the integrated vector control strategy is a continuous prevention method that succefully ensures the system free from dengue infection.