Optimal Control of The Spread of COVID-19 in Jakarta

Rizki Chika Audita Ariyani (An Nasher University)
Widowati Widowati (Universitas Diponegoro)
Uvi Dwian Kencono (Universitas An Nasher)
Lucky Cahya Wanditra (Universitas An Nasher)
Dhimas Mahardika (Universitas An Nasher)

M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika
Vol. 11 No. 2 (2026): Mathline : Jurnal Matematika dan Pendidikan Matematika

SARS-CoV-2 is the virus that causes COVID-19. In Indonesia, the highest number of COVID-19 cases is in the Jakarta province. It is necessary to restrict the virus's transmission. This research purposes to determine optimal control strategies (self-prevention, vaccination, and cure) of the SEAIQHRD model to reduce disease spread. Optimal control analysis is solved utilising Pontryagin's Minimum Principle. In this study, numerical simulations were conducted using COVID-19 outbreak data from Jakarta province from March 1 to August 31, 2022. Based on the analysis results, the basic reproduction number ℜ0 = 2,1316. Since ℜ0 > 1 at the EE point, the COVID-19 spread model is asymptotically stable, indicating that the virus persists in the population. The application of control steps combining all three strategies was shown to reduce the subpopulations of exposed, infected, hospitalized, and deceased individuals. Simultaneous optimal control is more effective at controlling the spread than using a control step. The simultaneous implementation of optimal controls has proven an effective strategy for reducing COVID-19 transmission in Jakarta.