An impulse fumigation scenario to control dengue spreads

Dengue fever is a disease caused by the bite of female Aedes aegypti mosquito which is infected by one of the four dengue viruses, namely DEN-1, DEN-2, DEN-3 or DEN-4. The disease has become a major priority of the WHO in recent years. Many efforts can be made to prevent dengue disease spreads. One of the efforts is to use fumigation to reduce the adult mosquito population. Unfortunately, fumigation intervention has many challenges. One of them is the budget limitation. To accomodate this problem, the optimal control theory will be implemented into the model of dengue disease spreads with fumigation intervention as the control variable. The purpose of this optimal control is to reduce the number of infected individuals and minimize the intervention cost. Characteristics of the optimal control is obtained by applying the Pontryagin principle. Furthermore, the optimal system is solved numerically by the Runge-Kutta method and the Gradient Descent method for the convergence criteria. It should be highlighted that the intervention (optimal control result) will be characterized as an impuls function to mimic the possibility of several strategies that might be implemented in the field.