Garuda - Garba Rujukan Digital

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

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

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

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.

APLICATION OF RAPID TEST CONTROL FOR PREVENTION PNEUMONIA IN CHILDREN Nilwan Andiraja; Adly Saddam Khadafi; Muhammad Firdaus; Vania Anjani; Dini Sahrani
Math Educa Journal Vol 9, No 2 (2025)
Publisher : UIN Imam Bonjol Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15548/mej.v9i2.12485

Pneumonia is a disease which is having similar symptoms like ISPA. It is probably that making many parents did not realize if their children severe Pneumonia. Because according to Indonesia ministry health, there was significant increasingly Pneumonia cases year by year from 2021 to 2024, in 2024 is a year with highest Pneumonia cases, almost 800.000 Pneumonia cases even BPJS report, budget for Pneumonia therapy is highest than other diseases. Then, we need to make a quick preventative action, one of them is optimal control with rapid test. Rapid test is needed in order to detect an individual severe Pneumonia. In order, the aim will success so we need to develop SEIR model with add a control of rapid test to the exposed class. The addition is needed because children have symptom acquiring a certainty Pneumonia infected or not so the therapy will be quick and correct. After that, we need to find the optimal control of rapid test and then to describe the effect of optimal control on the exposed, infected, and recovered classes. The parameters values need to input to the equations which was given a control and next, we have to calculate with used sweep method step forward-backward and with helped by MATLAB software obtain the final result. The result is with control the number individual infected Pneumonia decreasing since initial time till 100th days, meanwhile without control the number individual infected increase till 10th days and after that the plot becomes decrease till 40th days.

Title

Found 4 Documents
Search

Abstract

Abstract

Abstract

Abstract

Title Search

Found 4 Documents Search

Abstract

Abstract

Abstract

Abstract

Title

Found 4 Documents
Search