An optimum control model for resistance fumigation for dengue

In this article, we introduced an optimal control problem arising from differential equations for dengue which describe the spread of dengue in a region with a resistant mosquito population. The optimal control problem was constructed to handle a limited intervention budget, to reduce the number of infected humans and mosquitos. The Pontryagin Minimum Principle was used to formulate the optimal control problem, which was solved numerically with the forward-backward iterative method. The numerical simulation was performed with two scenarios, i.e., for different numbers of initially infected compartments (low and high) and for different numbers of initial basic reproduction (less than and greater than one). We find that fumigation intervention could be used to reduce the spread of dengue as long as the resistance of the mosquitos to the fumigant is low. We also found that fumigation intervention is much better in a prevention scenario since the cost function is much smaller than in a countermeasure scenario. Simulating the second scenario, we found that reducing the spread of dengue in a high risk area (basic reproduction number greater than one) is more costly than in a low risk area (basic reproduction number less than one).