Optimal Control of the Spread of Dengue Fever Using Dynamic Programming

Dengue fever is a disease caused by infection of the dengue virus. The virus is spread by a species of mosquito, namely Aedes Aegypti. Dengue fever can cause death to the sufferers. One of the possible methods to minimize the spread of dengue fever is controlling the cycle of Aedes Aegypti itself. This article simulates the use of temephos (some chemical substance) and fumigation to control the population growth of the adult mosquitoes. The first control, temephos, is given on the habitat of mosquito eggs and larvae. The second control, fumigation, is done by fogging on the habitat of mosquitoes. The problem is to determine which methods, i.e. the use of temephos or fumigation, are more effective to suppress the growth of the mosquito population. Here, we use a dynamic programming method to model the problem and to get an optimal control that can minimize some determined objective function. The numerical solution shows that both controls can be used to reduce the spread of the disease. However, it is apparent that fumigation is more effective.