Mathematical Model of COVID-19 with Aspects of Community Compliance to Health Protocols
DOI:
https://doi.org/10.25077/jmua.14.2.154-166.2025Keywords:
COVID-19, Health Protocols, Mathematical Models, Stability AnalysisAbstract
COVID-19 infection is still a health problem in various countries. Some people who recover from COVID-19 still experience some symptoms. Therefore, it is essential to implement health protocols to minimize transmission of the COVID-19 virus. Based on this, a mathematical model of COVID-19 with aspects of community compliance with health protocols is presented. The population is divided into three subpopulations: the susceptible subpopulation, the exposed subpopulation, and the infected subpopulation. The basic reproduction number, $R_0$, determines whether there are disease-free and endemic equilibrium points. When $R_0$ is less than 1, the disease-free equilibrium is locally asymptotically stable. Conversely, when $R_0$ is greater than 1, the endemic equilibrium point is locally stable. Numerical simulations will demonstrate how COVID-19 spreads, taking into account community adherence to health guidelines. The results of numerical simulations indicate that an increase in public adherence to health protocols leads to a decrease in the number of COVID-19 infections.
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Acheampong, E., Okyere, E., Iddi, S., Bonney, J. H. K., Asamoah, J. K. K., Wattis, J. A. D., & Gomes, R. L. (2022). Mathematical modelling of earlier stages of COVID-19 transmission dynamics in Ghana. Results in Physics, 34, 105193.
Atangana, A. (2021). Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world? Advances in Difference Equations, 2021(1), 403.
Balachandar, V., Mahalaxmi, I., Subramaniam, M., Kaavya, J., Kumar, N. S., Laldinmawii, G., Narayanasamy, A., Reddy, P. J. K., Sivaprakash, P., & Kanchana, S. (2020). Follow-up studies in COVID-19 recovered patients-is it mandatory? Science of the Total Environment, 729, 139021.
Bhadauria, A. S., Pathak, R., & Chaudhary, M. (2021). A SIQ mathematical model on COVID-19 investigating the lockdown effect. Infectious Disease Modelling, 6, 244–257.
Chumakov, K., Avidan, M. S., Benn, C. S., Bertozzi, S. M., Blatt, L., Chang, A. Y., Jamison, D. T., Khader, S. A., Kottilil, S., & Netea, M. G. (2021). Old vaccines for new infections: Exploiting innate immunity to control COVID-19 and prevent future pandemics. Proceedings of the National Academy of Sciences, 118(21), e2101718118.
Ega, T. T., & Ngeleja, R. C. (2022). Mathematical Model Formulation and Analysis for COVIDâ€19 Transmission with Virus Transfer Media and Quarantine on Arrival. Computational and Mathematical Methods, 2022(1), 2955885.
Elhiny, R., Al-Jumaili, A. A., & Yawuz, M. J. (2022). What might COVID-19 patients experience after recovery? A comprehensive review. International Journal of Pharmacy Practice, 30(5), 404–413.
Fajrah, S. (2022). Covid-19 Health Protocol Education for Health Cadres and the Community. Frontiers in Community Service and Empowerment, 1(2), 46–51.
Frost, I., Craig, J., Osena, G., Hauck, S., Kalanxhi, E., Schueller, E., Gatalo, O., Yang, Y., Tseng, K. K., & Lin, G. (2021). Modelling COVID-19 transmission in Africa: countrywise projections of total and severe infections under different lockdown scenarios. BMJ Open, 11(3), e044149.
Fu, Y., Xiang, H., Jin, H., & Wang, N. (2021). Mathematical modelling of lockdown policy for covid-19. Procedia Computer Science, 187, 447–457.
Task Force for the Acceleration of Handling COVID-19. (2023), November 6). https: //covid19.go.id/
Iqbal, A., Iqbal, K., Ali, S. A., Azim, D., Farid, E., Baig, M. D., Arif, T. Bin, & Raza, M. (2021). The COVID-19 sequelae: a cross-sectional evaluation of post-recovery symptoms and the need for rehabilitation of COVID-19 survivors. Cureus, 13(2).
Kolebaje, O. T., Vincent, O. R., Vincent, U. E., & McClintock, P. V. E. (2022). Nonlinear growth and mathematical modelling of COVID-19 in some African countries with the Atangana–Baleanu fractional derivative. Communications in Nonlinear Science and Numerical Simulation, 105, 106076.
Kurniawan, E. A. D., Fatmawati, F., & Dianpermatasari, A. (2021). Model Matematika SEAR dengan Memperhatikan Faktor Migrasi Terinfeksi untuk Kasus COVID-19 di Indonesia. Limits: Journal of Mathematics and Its Applications, 18(2), 142–153.
Li, M., Wang, H., Tian, L., Pang, Z., Yang, Q., Huang, T., Fan, J., Song, L., Tong, Y., & Fan, H. (2022). COVID-19 vaccine development: milestones, lessons and prospects. Signal Transduction and Targeted Therapy, 7(1), 146.
Prioleau, T. (2021). Learning from the experiences of covid-19 survivors: web-based survey study. JMIR Formative Research, 5(5), e23009.
Rajput, A., Sajid, M., Tanvi, Shekhar, C., & Aggarwal, R. (2021). Optimal control strategies on COVID-19 infection to bolster the efficacy of vaccination in India. Scientific Reports, 11(1), 20124.
Sinaga, L. P., Kartika, D., & Nasution, H. (2021). Pengantar Sistem Dinamik. Amal Insani Publisher.
Singh, V. (2020). A review on acute respiratory syndrome corona virus 2 (SARS-Cov-2) & its preventive management. Asian Journal of Pharmaceutical Research and Development, 8(3), 142–151.
Van den Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1–2), 29–48.
Wangari, I. M., Sewe, S., Kimathi, G., Wainaina, M., Kitetu, V., & Kaluki, W. (2021). Mathematical Modelling of COVID-19 Transmission in Kenya: A Model with Reinfection Transmission Mechanism. Computational and Mathematical Methods in Medicine, 2021(1), 5384481.
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