Optimal Control of Dengue Fever Disease Spread Model Using Pontryagin Minimum Principle
DOI:
https://doi.org/10.15575/kubik.v11i1.44998Abstract
Dengue hemorrhagic fever (DHF) is one of the major health problems in Indonesia. The spread of DHF will increase during the rainy season because the Aedes Aegypti mosquito as the main vector of disease spread will lay eggs and hatch their eggs in stagnant water so that they become mosquito larvae. The spread of DHF can be controlled by administering larvicides and the 3M movement (drain, cover, bury water storage containers) to reduce the population of infected humans and mosquitoes. In this study, the epidemic model is divided into six subpopulations namely Susceptible Host , Infected Host , Recovered Host , Aquatic phase , Susceptible vector and Infected vector . From the six subpopulations, an epidemic model is then formed by providing control. Furthermore, the optimal control method is applied based on the Pontryagin minimum principle method so that an optimal control is obtained and is obtained. Furthermore, the numerical solution is solved using the fourth-order Sweep Forward-Backward Runge Kutta method with the help of Python software. Based on the analysis and simulation results, it is shown that without control, the spread of dengue disease between humans and mosquitoes is rapid, with a sharp increase in the infected population. Implementing control measures such as larvicide application and 3M movement effectively reduces the number of infected humans and mosquitoes to very low throughout the simulation.
Keywords: Optimal Control, DHF Disease Model, Pontryagin Minimum Principle
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Copyright (c) 2026 Oktavia Arnelliza Ayu, Bayu Prihandono, Nilamsari Kusumastuti
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