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All Journal Kubik Justek : Jurnal Sains Dan Teknologi KUBIK: Jurnal Publikasi Ilmiah Matematika
Nilwan Andiraja
UIN Sultan Syarif Kasim Riau
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Mathematics

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Optimal Control of Vaccination for Dengue Fever in SIR Model Nilwan Andiraja; Sri Basriati; Elfira Safitri; Rahmadeni Rahmadeni; A Martino
KUBIK Vol 7, No 2 (2022): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v7i2.21397

Abstract

According to data from The Indonesian ministry of health, many of individuals suffere dengue fever until may 2023 in Indonesia. To reduce its cases, in this article, a single of control strategy of vaccination for infected human by dengue fever has been proposed. To obtain the optimal control, the SIR model has been modificated with single control and the new objective function has been made before the Pontryagin minimum principle is used in this article. According to the differential equation in the model of the dengue fever and the objective function, we made the Hamiltonian equation. Then, from it, the state equation, costate equation, and stationary condition has been made from the Hamiltonian equation so we obtained the optimal control in vaccination. In the end of this article, we did the numerical simulation using the sweep forward-backward method. Through numerical simulation, we find that the control succeed to reduce the infected human by dengue fever and also increase human recovery from this desease. Futhermore, the control of vaccination for infected human should be implemented not only in this mathematical model but also into real life to decrease the dengue fever case. 
Optimal Control of Vaccination for Dengue Fever in SIR Model Nilwan Andiraja; Sri Basriati; Elfira Safitri; Rahmadeni Rahmadeni; Alfitra Martino
KUBIK Vol 7, No 2 (2022): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v7i2.21397

Abstract

According to data from The Indonesian ministry of health, many of individuals suffere dengue fever until may 2023 in Indonesia. To reduce its cases, in this article, a single of control strategy of vaccination for infected human by dengue fever has been proposed. To obtain the optimal control, the SIR model has been modificated with single control and the new objective function has been made before the Pontryagin minimum principle is used in this article. According to the differential equation in the model of the dengue fever and the objective function, we made the Hamiltonian equation. Then, from it, the state equation, costate equation, and stationary condition has been made from the Hamiltonian equation so we obtained the optimal control in vaccination. In the end of this article, we did the numerical simulation using the sweep forward-backward method. Through numerical simulation, we find that the control succeed to reduce the infected human by dengue fever and also increase human recovery from this desease. Futhermore, the control of vaccination for infected human should be implemented not only in this mathematical model but also into real life to decrease the dengue fever case. 
Application of Mosquito Net Control in a New Dynamics of Dengue Nilwan Andiraja
Justek : Jurnal Sains dan Teknologi Vol 9, No 2 (2026): June
Publisher : Unversitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/justek.v9i2.39546

Abstract

This study discusses the application of mosquito net control in the SIR-UV model for the spread of dengue fever. The study has a specific objective to analyze the effectiveness of mosquito net control on the vulnerable human population to reduce the number of people infected with dengue fever. This research begins by forming a new SIR-UV mathematical model (state equation) with mosquito net control in the class of vulnerable human population and creating a new objective function to minimize the population of humans infected with dengue fever. Next, using Pontryagin's principle, the Hamiltonian function was formed. From the Hamiltonian function, the costate equation and the optimal control for the use of mosquito nets were obtained. The next step is to change the state equation and the costate equation using the 4th order Runge-Kutta method. Then a numerical simulation is performed, with the forward sweep method determining the solution to the state equation, and the backward sweep method for solving the costate equation. Numerical simulations will be conducted to observe the effects of control on the class of human population infected. The numerical simulations will use some data from previous research so that the simulation results can be compared with the previous research findings. The simulation results show that the use of mosquito nets on the vulnerable human population class can reduce the population of humans infected with dengue fever, where from the initial time of day 0, the graph of infected humans immediately drops below 20 days and continues to approach zero until day 100. It has same results for mosquitoes infected, which decreased immediately from the start continued to approach zero until days 100. In contrast, without control, there is a spike in the number of infected humans at the beginning and will approach zero by day 80 and it took until day 60 for the mosquitoes infected population with dengue virus to approach 0. Therefore, the use of mosquito nets on the vulnerable human population can reduce the number of humans infected with dengue fever and, of course, contribute to minimizing the spread of dengue fever.
Co-Authors A Martino Alfitra Martino Elfira Safitri Rahmadeni Rahmadeni Sri Basriati