Optimal Control of Vaccination for Dengue Fever in SIR Model

Nilwan Andiraja, Sri Basriati, Elfira Safitri, Rahmadeni Rahmadeni, A. Martino
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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. 
SIR模型中登革热疫苗接种的最优控制
根据印度尼西亚卫生部的数据,印度尼西亚许多人在2023年5月之前患有登革热。为减少登革热病例,本文提出了登革热感染者接种登革热疫苗的单一控制策略。为了获得最优控制,本文在采用庞特里亚金最小原理之前,对SIR模型进行了单控制修正,并建立了新的目标函数。根据登革热模型中的微分方程和目标函数,建立了哈密顿方程。在此基础上,由哈密顿方程导出了状态方程、协态方程和平稳条件,从而得到了疫苗接种的最优控制。在本文的最后,我们使用正向向后扫描的方法进行了数值模拟。通过数值模拟,我们发现控制成功地减少了登革热的感染人数,也增加了人类从这种疾病的恢复。此外,对感染者的疫苗接种控制不仅要在数学模型中实施,而且要在实际生活中实施,以减少登革热病例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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