Modeling the Dynamics of Cardiovascular Disease Using a SEICRD Framework

Arista Fitri Diana, Mia Siti Khumaeroh, Tarita Intan Soraya

Abstract


Cardiovascular disease remains a major public health challenge worldwide, often progressing silently toward chronic complications. Increasing awareness through media and individual behavioral responses plays an important role in preventing disease transmission and reducing long-term complications. Motivated by this, we formulate a deterministic compartmental model to investigate the dynamics of cardiovascular disease by incorporating media awareness and individual awareness as control-related parameters. The population is divided into susceptible, exposed, infected, chronic, recovered, and deceased compartments. A qualitative analysis of the linear dynamical system is carried out, including positivity of solutions, bound- edness, equilibrium points, and local stability analysis using eigenvalue criteria. Numerical simulations are performed to illustrate the effects of key epidemiological and awareness-related parameters on disease progression. The simulation results indicate that increased media and individual awareness significantly reduce the long-term burden of chronic cardiovascular complications. In contrast, higher incidence and disease progression rates lead to increased accumulation in the chronic compartment, even when the number of active infections declines more rapidly. Sensitivity analysis confirms that awareness parameters have a negative influ- ence on chronic disease prevalence, whereas core epidemiological parameters exert a strong positive effect. These findings highlight the critical role of awareness-based interventions in mitigating chronic cardiovascular disease and provide a quantitative framework to support effective prevention and control strategies.

Keywords


Cardiovascular disease; Dynamical system; Stability analysis; Epidemiological; Sensitivity analysis.

Full Text:

PDF

References


[1] O. R. Ojo, H. O. Francis, M. O. Awoleye, J. Chimezie, W. O. Agbonifo, and T. G. Adedeji. “A Scoping Review on Mathematical Modelling Techniques Used in Non-communicable Disease (NCD) Research”. Advances in Research 26.3 (2025), pp. 437–458. DOI: https://doi.org/10.9734/air/2025/v26i31361.

[2] C. E. Agbo, R. T. Abah, and A. M. Abdullahi. “A Mathematical Modeling on the Stability Analysis of Heart Disease Dynamics”. Journal of Institutional Research, Big Data Analytics and Innovation 1.1 (2024), pp. 195–202. URL: https://fnasjournals.com/index.php/FNAS-JMNS/article/view/776/693.

[3] L. Ciumrnean et al. “Cardiovascular Risk Factors and Physical Activity for the Prevention of Cardiovascular Diseases in the Elderly”. International Journal of Environmental Research and Public Health 19.1 (2022). DOI: https://doi.org/10.3390/ijerph19010207.

[4] D. Plass et al. “Estimating Risk Factor Attributable Burden: Challenges and Potential Solutions When Using the Comparative Risk Assessment Methodology”. Archives of Public Health 80.1 (2022), pp. 1–12. DOI: https://doi.org/10.1186/s13690-022-00900-8.

[5] L. Jibril and O. Odetunde. “Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD)”. Biomedical Statistics and Informatics 5.4 (2020), p. 87. DOI: https://doi.org/10.11648/j.bsi.20200504.13.

[6] Cheffer. Analysis of Cardiovascular Rhythms Using Mathematical Models. PDF document. URL: http://mecanon.coppe.ufrj.br/wp-content/uploads/2017/08/Heart-Cardiology_JCCM-21.pdf.

[7] D. Roy, O. Mazumder, A. Sinha, and S. Khandelwal. “Multimodal Cardiovascular Model for Hemodynamic Analysis: Simulation Study on Mitral Valve Disorders”. PLOS ONE 16.3 (2021), pp. 1–28. DOI: https://doi.org/10.1371/journal.pone.0247921.

[8] A. Arzani and S. T. M. Dawson. “Data-Driven Cardiovascular Flow Modelling: Examples and Opportunities”. Journal of the Royal Society Interface 18.175 (2021). DOI: https://doi.org/10.1098/rsif.2020.0802.

[9] S. G. Hafezi et al. New Dynamic Approach Models to Estimate the Effect of Dietary Fatty Acids on Lipid Profiles and the Incidence of Cardiovascular Disease in the MASHAD Cohort Study. Research Square. 2023. URL: https://www.researchsquare.com/article/rs-3172809/v1.

[10] S. Lishak, G. Grigorian, S. V. George, N. C. Ovenden, R. J. Shipley, and S. Arridge. “A Variable Heart Rate Multi-Compartmental Coupled Model of the Cardiovascular and Respiratory Systems”. Journal of the Royal Society Interface 20.207 (2023). DOI: https://doi.org/10.1098/rsif.2023.0339.

[11] N. W. Jannah, L. Aryati, and F. Adi-Kusumo. “A Mathematical Model of Social Interaction Between the Sufferers of Cardiovascular and Type 2 Diabetes Mellitus”. Communications in Biomathematical Sciences 7.1 (2024), pp. 87–105. DOI: https://doi.org/10.5614/cbms.2024.7.1.5.

[12] J. M. Mutwiwa. “A Mathematical Model of Cardiovascular Disease Dynamics Incorporating Personal Risk Factors”. Asian Journal of Probability and Statistics 27.6 (2025), pp. 74–83. DOI: https://doi.org/10.9734/ajpas/2025/v27i6768.

[13] M. Logambal, S. Padmasekaran, and S. Dickson. “Evaluation of the Stability of Heart Disease Mathematical Model: The Impact of Heart Attack and Chronic Heart Disease”. Proyecciones 44.5 (2025), pp. 742–761. DOI: https://doi.org/10.22199/issn.0717-6279-6812.

[14] S. Y. Tee and A. A. M. Daud. “Mathematical Model and Analysis of Population Dynamics for Heart Failure and Heart Transplant”. Journal of Quality Measurement and Analysis 21.1 (2025), pp. 69–85. DOI: https://doi.org/10.17576/jqma.2101.2025.04.

[15] A. F. Diana, T. I. Soraya, M. S. Khumaeroh, and M. I. Hajar. “Optimal Control of Cardiovascular Disease Using Pontryagin’s Maximum Principle”. ZERO: Jurnal Sains, Matematika dan Terapan 9.2 (2025), p. 443. DOI: https://doi.org/10.30829/zero.v9i2.25849.

[16] A. A. Zainuddin et al. “The Major Risk Factor of Stroke Across Indonesia; A Nationwide Geospatial Analysis of Universal Health Coverage Program”. Archives of Public Health 83.1 (2025). DOI: https://doi.org/10.1186/s13690-025-01613-4.

[17] J. Y. Lee et al. “Long-Term Cardiovascular Events in Hypertensive Patients: Full Report of the Korean Hypertension Cohort”. Korean Journal of Internal Medicine 38.1 (2023), pp. 56–67. DOI: https://doi.org/10.3904/kjim.2022.249.

[18] World Health Organization. World Health Statistics 2025. 2025. URL: https://www.who.int/publications/b/78420.

[19] E. S. Darmawan, S. R. Hasibuan, V. Y. Permanasari, and D. Kusuma. “Disparities in Cancer Care and Outcomes by Insurance Membership Type in Indonesia: A Retrospective Cross-Sectional Analysis of National Health Insurance Claims, 2017–2022”. BMJ Open 15.7 (2025). DOI: https://doi.org/10.1136/bmjopen-2024-096486.

[20] F. R. Muharram et al. “The 30 Years of Shifting in The Indonesian Cardiovascular Burden—Analysis of The Global Burden of Disease Study”. Journal of Epidemiology and Global Health 14.1 (2024), pp. 193–212. DOI: https://doi.org/10.1007/s44197-024-00187-8.

[21] B. Dwiputra et al. “Risk Estimation for Recurrent Cardiovascular Events Using the SMART-REACH Model and Direct Inpatient Cost Profiling in Indonesian ASCVD Patients: A Large-Scale Multicenter Study”. Frontiers in Cardiovascular Medicine 11.August (2024), pp. 1–9. DOI: https://doi.org/10.3389/fcvm.2024.1425703.

[22] W. Frk, A. Wojtasiska, W. Lisiska, E. Mynarska, B. Franczyk, and J. Rysz. “Pathophysiology of Cardiovascular Diseases: New Insights into Molecular Mechanisms of Atherosclerosis, Arterial Hypertension, and Coronary Artery Disease”. Biomedicines 10.8 (2022). DOI: https://doi.org/10.3390/biomedicines10081938.

[23] World Health Organization. World Health Statistics 2019. Bibliographic data in the source list is incomplete. 2019. URL: file:///Users/macbook/Downloads/547-Article%20Text-2022-1-10-20200417.pd.

[24] Badan Pusat Statistik. Badan Pusat Statistik Provinsi Jawa Tengah Dalam Angka 2020. Vol. 3, No. 2, p. 861. 2020. URL: https://bit.ly/4tYFHnB.

[25] Pemerintah Provinsi Jawa Tengah. Laporan Demografi Jawa Tengah Tahun 2021. 2021. URL: https://bit.ly/4wPzY6b.

[26] Adhi Wiriana. Laporan Demografi Jawa Tengah Tahun 2022. 2022. URL: https://jateng.bps.go.id/id/publication/2022/02/25/431f4f4bbe02b47866b357cc/provinsi-jawa-tengah-dalam-angka-2022.html.

[27] Dinas Pemberdayaan Masyarakat dan Provinsi Jawa Tengah. Laporan Demografi Jawa Tengah Tahun 2023. 2023. URL: https://bit.ly/4dyEVZy.

[28] Dinas Kesehatan Jawa Tengah. Laporan Demografi Jawa Tengah Tahun 2024. Profil Kesehatan Provinsi Jawa Tengah Tahun 2024, Vol. 3, pp. 1–260. 2024. URL: https://bit.ly/4dBJvVy.

[29] E. Astutik, S. I. Puspikawati, D. M. S. K. Dewi, A. M. Mandagi, and S. K. Sebayang. “Prevalence and Risk Factors of High Blood Pressure Among Adults in Banyuwangi Coastal Communities, Indonesia”. Ethiopian Journal of Health Sciences 30.6 (2020), pp. 941–950. DOI: https://doi.org/10.4314/ejhs.v30i6.12.

[30] Food Technology. “Coronary artery disease incidence, risk factors, awareness, and medication utilization in a 10-year cohort study”. BMC Cardiov. Bibliographic data in the source list is incomplete.




DOI: https://doi.org/10.18860/cauchy.v11i1.41645

Refbacks

  • There are currently no refbacks.


Copyright (c) 2026 Arista Fitri Diana, Mia Siti Khumaeroh, Tarita Intan Soraya

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.