Optimal control on education, vaccination, and treatment in the model of dengue hemorrhagic fever

Abstract

Dengue hemorrhagic fever (DHF) is an infection caused by the dengue virus which is transmitted by the Aedes aegypti mosquito. In this paper, a model of the spread of dengue disease is developed using optimal control theory by dividing the population into Susceptible, Exposed, Infected, and Recovered (SEIR) sub-populations. The Pontryagin minimum principle of the fourth-order Runge-Kutta method is used in the model of the spread of dengue disease by incorporating control factors in the form of education and vaccination of susceptible human populations, as well as treatment of infected human populations. Optimum control aims to minimize the infected human population in order to reduce the spread of DHF. Simulations were carried out for two cases, namely when the basic reproduction number   is less than one for disease-free conditions and  greater than one for endemic conditions. Based on numerical simulations of the SEIR epidemic model with controls, it results that the optimal strategy is achieved if education controls, vaccinations, and medication are used.