UNDERSTANDING THE DYNAMICS OF COVID-19 TRANSMISSION IN PAMPANGA PHILIPPINES: MODELING WITH A SYSTEM OF DIFFERENTIAL EQUATIONS

Main Article Content

Aldrin P. Mendoza

Abstract

This study introduced and solved a system of differential equations aimed at modeling the coronavirus disease 2019 (COVID-19) transmission dynamics in the province of Pampanga. Specifically, a Susceptible, Infected, Recovered, Deceased (SIRD) model was developed and built upon the foundational SIR model devised by Kermack and McKendrick in 1927.1 Various methods were employed to solve the model. Initially, the analytical solution for the rate of change of infected individuals over time  was determined. Subsequently, model parameters were identified through an optimization process using the Microsoft Excel Solver. The Runge-Kutta fourth order (RK4) method, implemented in Scilab 6.1.1, was utilized to approximate the numerical solution for the rates of change of susceptible , recovered , and deceased  over time. The findings underscored the significance of several parameters—namely, the transmission rate , removal rate (combining recovery  and deceased rate ), the proportion of the infected population properly wearing face masks , the proportion disinfecting regularly , and the proportion practicing isolation or social distancing —in shaping the transmission dynamics of COVID-19 in Pampanga. The values of these model parameters reflect the effectiveness of governmental responses and actions in managing, controlling, and mitigating the spread of COVID-19, as well as the extent of public cooperation and compliance with COVID-19 directives and advisories.

Keywords: COVID-19, Differential Equations, Runge-Kutta fourth order (RK4) method, SIRD model

Article Details

How to Cite
MENDOZA, Aldrin P.. UNDERSTANDING THE DYNAMICS OF COVID-19 TRANSMISSION IN PAMPANGA PHILIPPINES: MODELING WITH A SYSTEM OF DIFFERENTIAL EQUATIONS. Medical Research Archives, [S.l.], v. 12, n. 1, jan. 2024. ISSN 2375-1924. Available at: <https://esmed.org/MRA/mra/article/view/5066>. Date accessed: 03 mar. 2024. doi: https://doi.org/10.18103/mra.v12i1.5066.
Section
Research Articles

References

1. Kermack, W. O., & McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character, 115(772), 700-721.

2. Huppert, A., & Katriel, G. (2013). Mathematical modelling and prediction in infectious disease epidemiology. Clinical Microbiology and Infection, 19(11), 999–1005. https://doi.org/10.1111/1469-0691.12308

3. Tolles, J., & Luong, T. (2020). Modeling Epidemics With Compartmental Models. JAMA, 323(24), 2515. https://doi.org/10.1001/jama.2020.8420

4. Alanazi, S. A., Kamruzzaman, M. M., Alruwaili, M., Alshammari, N., Alqahtani, S. A., & Karime, A. (2020). Measuring and Preventing COVID-19 Using the SIR Model and Machine Learning in Smart Health Care. Journal of Healthcare Engineering, 2020, 1–12. https://doi.org/10.1155/2020/8857346

5. Ambikapathy, B., & Krishnamurthy, K. (2020). Mathematical Modelling to Assess the Impact of Lockdown on COVID-19 Transmission in India: Model Development and Validation. JMIR Public Health and Surveillance, 6(2), e19368. https://doi.org/10.2196/19368

6. Beira MJ, Sebastião PJ. A differential equations model-fitting analysis of COVID-19 epidemiological data to explain multi-wave dynamics. Scientific Reports. 2021;11(1). doi:https://doi.org/10.1038/s41598-021-95494-6

7. Caldwell, J. M., de Lara-Tuprio, E., Teng, T. R., Estuar, M. R. J. E., Sarmiento, R. F. R., Abayawardana, M., Leong, R. N. F., Gray, R. T., Wood, J. G., Le, L.-V., McBryde, E. S., Ragonnet, R., & Trauer, J. M. (2021). Understanding COVID-19 dynamics and the effects of interventions in the Philippines: A mathematical modelling study. The Lancet Regional Health - Western Pacific, 14, 100211. https://doi.org/10.1016/j.lanwpc.2021.100211

8. Garrido, J. M., Martínez-Rodríguez, D., Rodríguez-Serrano, F., Pérez-Villares, J. M., Ferreiro-Marzal, A., Jiménez-Quintana, M. M., & Villanueva, R. J. (2022). Mathematical model optimized for prediction and health care planning for COVID-19. Medicina Intensiva (English Edition). https://doi.org/10.1016/j.medine.2022.02.020

9. Hao, X., Cheng, S., Wu, D. et al. Reconstruction of the full transmission dynamics of COVID-19 in Wuhan. Nature 584, 420–424 (2020). https://doi.org/10.1038/s41586-020-2554-8

10. Meiksin A. Dynamics of COVID-19 transmission including indirect transmission mechanisms: a mathematical analysis. Epidemiol Infect. 2020 Oct 23;148:e257. doi: 10.1017/S0950268820002563.
PMID: 33092672; PMCID: PMC7642914.

11. Mpinganzima L, Ntaganda JM, Banzi W, Muhirwa JP, Nannyonga BK, Niyobuhungiro J, Rutaganda E. Analysis of COVID-19 mathematical model for predicting the impact of control measures in Rwanda. Inform Med Unlocked. 2023;37:101195. doi: 10.1016/j.imu.2023.101195. Epub 2023 Feb 13. PMID: 36819990; PMCID: PMC9930676.

12. Tibane, N., Makinde, O. D., & Monaledi, R. (2023). Dynamics of Covid-19 disease with its economic implications and optimal control: An exploitation of variational iteration method. Informatics in Medicine Unlocked, 42, 101356. https://doi.org/10.1016/j.imu.2023.101356

13. Zakary, O., Bidah, S., Rachik, M., & Ferjouchia, H. (2020). Mathematical Model to Estimate and Predict the COVID-19 Infections in Morocco: Optimal Control Strategy. J. Appl. Math., 2020, 9813926:1-9813926:13.

14. Goswami GG, Labib T. Modeling COVID-19 Transmission Dynamics: A Bibliometric Review. Int J Environ Res Public Health. 2022 Oct 29;19(21):14143. doi: 10.3390/ijerph192114143. PMID: 36361019; PMCID: PMC9655715.

15. Mourmouris P, Tzelves L, Roidi C, Fotsali A. COVID-19 transmission: a rapid systematic review of current knowledge. Osong Public Health Res Perspect. 2021 Apr;12(2):54-63. doi: 10.24171/j.phrp.2021.12.2.02. Epub 2021 Apr 29. PMID: 33979995; PMCID: PMC8102883.

16. Cooper I, Mondal A, Antonopoulos CG. A SIR model assumption for the spread of COVID-19 in different communities. Chaos, Solitons & Fractals. 2020;139:110057. doi:https://doi.org/10.1016/j.chaos.2020.110057

17. Mallari KS, Mendoza A. A System of Differential Equations Modeling COVID-19 Transmission Dynamics in Pampanga. SSRN Electronic Journal. Published online 2022. doi:https://doi.org/10.2139/ssrn.4212122

18. de Roquetaillade, C., Bredin, S., Lascarrou, J.-B., Soumagne, T., Cojocaru, M., Chousterman, B. G., Leclerc, M., Gouhier, A., Piton, G., Pène, F., Stoclin, A., & Llitjos, J.-F. (2021). Timing and causes of deceased in severe COVID-19 patients. Critical Care, 25, 224. https://doi.org/10.1186/s13054-021-03639-w

19. cdc.gov/coronavirus. (n.d.). Retrieved December 20, 2023, from https://www.cdc.gov/coronavirus/2019-ncov/downloads/COVID19-symptoms.pdf#:~:text=Know%20the%20symptoms%20of%20COVID-19%2C%20which%20can%20include

20. Weisstein, E. W. (n.d.). Runge-Kutta Method. Mathworld.wolfram.com. https://mathworld.wolfram.com/Runge-KuttaMethod.html

21. 3.3: The Runge-Kutta Method. (2020, January 7). Mathematics LibreTexts. https://math.libretexts.org/Courses/Monroe_Community_College/MTH_225_Differential_Equations/3%3A_Numerical_Methods/3.3%3A_The_Runge-Kutta_Method

22. Runge-Kutta 4th Order Method to Solve Differential Equation - GeeksforGeeks. (2016, January 31). GeeksforGeeks. https://www.geeksforgeeks.org/runge-kutta-4th-order-method-solve-differential-equation/