KUBIK: Jurnal Publikasi Ilmiah Matematika
Vol 11 No 1 (2026): KUBIK: Jurnal Publikasi Ilmiah Matematika

Kontrol Optimal Model Penyebaran Penyakit Demam Berdarah Dengue Menggunakan Prinsip Minimum Pontryagin

Oktavia Arnelliza Ayu (Universitas Tanjungpura)
Bayu Prihandono (Universitas Tanjungpura)
Nilamsari Kusumastuti (Universitas Tanjungpura)



Article Info

Publish Date
30 May 2026

Abstract

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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Journal Info

Abbrev

kubik

Publisher

Subject

Computer Science & IT Economics, Econometrics & Finance Mathematics

Description

Fuzzy Systems and its Applications Geometry Theories and its Applications Graph Theories and its Applications Real Analysis and its Applications Operation Research and its Applications Statistical Theories and its Applications Dinamical Systems and its Applications Mathematics Modeling and its ...