Optimal Control of Cardiovascular Disease Using Pontryagin’s Maximum Principle

Diana, Arista Fitri (Department of Actuarial Science, Institut Teknologi Statistika dan Bisnis Muhammadiyah Semarang, 50181, Indonesia)
Soraya, Tarita Intan (Department of Actuarial Science, Institut Teknologi Statistika dan Bisnis Muhammadiyah Semarang, 50181, Indonesia)
Khumaeroh, Mia Siti (Department of Mathematics, Universitas Islam Negeri Sunan Gunung Djati, Bandung, 40614, Indonesia)
Hajar, Muhammad Ibnu (Department of Actuarial Science, Institut Teknologi Statistika dan Bisnis Muhammadiyah Semarang, 50181, Indonesia)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 9, No 2 (2025): Zero: Jurnal Sains Matematika dan Terapan

Cardiovascular disease poses serious global health and economic challenges. This study develops a dynamic model by adapting the infectious-disease SEIR framework to a non-communicable disease context and extending it with a hospitalized compartment. Three control strategies: curative intervention (u1), lifestyle modification (u2), and preventive screening–education (u3) are incorporated and optimized using Pontryagin’s Maximum Principle. Numerical simulations, calibrated with data from Rinkendiknas, World Health Organization, National Health Insurance program, BMC Public Health, National Library of Medicine, and RS Roemani Muhammadiyah Semarang, show that curative control rapidly reduces early case burden, while lifestyle modification and education sustain long-term declines. With combined controls, the exposed, infected, and hospitalized compartments decrease by 10%, 20,8%, and 7,4%, respectively, while costs are reduced by 28,5% compared to single interventions. The integration of epidemiological models, health-system dynamics, and multi-control optimization offers both methodological novelty and practical value for cost-effective cardiovascular disease policy design.