Optimal control of dengue fever model with a logistically growing human population

Dengue is a deadly illness in almost all parts of Indonesia, including East Java. This paper analyzes the dengue transmission model by considering the recruitment rate in the form of the logistic growth of the human population. The model parameters were estimated using least-squares methods based on dengue data in East Java, Indonesia. The model analysis results obtained two equilibria, namely the diseases-free and the endemic equilibria. The disease-free equilibrium is asymptotically stable if the basic reproduction number $R_0$ $<$ 1, while the endemic equilibrium is asymptotically stable if $R_0$ $>$ 1. The control variables were incorporated, and an optimal control problem was analyzed using the Pontryagin maximum principle. Finally, the cost-effectiveness analysis suggests that prevention only is the the most cost-effective strategy required to control dengue disease.