Mathematical Modeling of Epidemic Spread: COVID-19 Case ‎Study and Future Pandemic Preparedness

  • Authors

    • Dadaso T. Man‎e Assistant professor, Department of Information Technology, Rajarambapu Institute of Technology, Rajaramnagar, Sakharale, India ‎2 Associate professor, AISSMS IOIT, Pune, India‎
    • Kishor S. Wagh Associate professor, AISSMS IOIT, Pune, India
    • Kavita Tukaram Patil Assistant Professor, Department of Computer Engineering, SVKM's Institute of Technology, Dhule-424001, India
    • Tanuja Satish Dhope Bharati Vidyapeeth (Deemed to be University) College of Engineering, Pune, India
    • Nilesh D. Mali Ajeenkya D.Y.Patil School of Engineering, Pune, India
    • Nanda Satish Kulkarni iddhant College of Engineering, Pune, India
    • Deepak Gupta Department of Computer Science, ITM Gwalior, India‎
    https://doi.org/10.14419/7tx0yh53

    Received date: June 8, 2025

    Accepted date: July 7, 2025

    Published date: July 15, 2025

  • COVID-19; Disease Dynamics; Epidemic Modeling; Mathematical Biology; SEIR Model‎.

  • Abstract

    This paper presents a comprehensive mathematical framework for modeling epidemic spread, with a specific application to the COVID-19 ‎pandemic. We develop an enhanced SEIR (Susceptible-Exposed-Infected-Recovered) model incorporating vaccination dynamics, behavioral ‎changes, and spatial heterogeneity. Our model introduces time-varying transmission rates and accounts for asymptomatic carriers, providing ‎more accurate predictions than traditional compartmental models. Through numerical simulations calibrated with real-world COVID-19 data ‎from multiple countries, we demonstrate the model's effectiveness in capturing complex epidemic dynamics. The framework achieves a ‎prediction accuracy of 92.3% for peak timing and 87.6% for case counts over a 60-day horizon. We further extend the model to incorporate ‎machine learning techniques for parameter estimation, resulting in improved forecasting capabilities. Our findings reveal critical insights for ‎pandemic preparedness, including the optimal timing of interventions and the impact of population heterogeneity on disease spread. This ‎work provides policymakers with a robust tool for epidemic management and highlights key areas for future pandemic preparedness ‎strategies‎.

  • References

    1. Anderson, R. M., Heesterbeek, H., Klinkenberg, D., & Hollingsworth, T. D. (2020). "How will country-based mitigation measures influence the course of the COVID-19 epidemic?" The Lancet, 395(10228), 931-934. https://doi.org/10.1016/S0140-6736(20)30567-5.
    2. Ferguson, N. M., Laydon, D., Nedjati-Gilani, G., et al. (2020). "Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand." Imperial College COVID-19 Response Team, Report 9.
    3. Kermack, W. O., & McKendrick, A. G. (1927). "A contribution to the mathematical theory of epidemics." Proceedings of the Royal Society A, 115(772), 700-721. https://doi.org/10.1098/rspa.1927.0118.
    4. Brauer, F., Castillo-Chavez, C., & Feng, Z. (2019). Mathematical Models in Epidemiology. Springer-Verlag, New York. https://doi.org/10.1007/978-1-4939-9828-9.
    5. Diekmann, O., Heesterbeek, J. A. P., & Metz, J. A. (2000). "On the definition and the computation of the basic reproduction ratio R₀." Journal of Mathematical Biology, 41(4), 365-382.
    6. Hethcote, H. W. (2000). "The mathematics of infectious diseases." SIAM Review, 42(4), 599-653. https://doi.org/10.1137/S0036144500371907.
    7. Li, Q., Guan, X., Wu, P., et al. (2020). "Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia." New England Journal of Medicine, 382(13), 1199-1207. https://doi.org/10.1056/NEJMoa2001316.
    8. Wu, J. T., Leung, K., & Leung, G. M. (2020). "Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV out-break." The Lancet, 395(10225), 689-697. https://doi.org/10.1016/S0140-6736(20)30260-9.
    9. Davies, N. G., Klepac, P., Liu, Y., et al. (2020). "Age-dependent effects in the transmission and control of COVID-19 epidemics." Nature Medi-cine, 26(8), 1205-1211. https://doi.org/10.1038/s41591-020-0962-9.
    10. Moghadas, S. M., Shoukat, A., Fitzpatrick, M. C., et al. (2020). "Projecting hospital utilization during the COVID-19 outbreaks in the United States." PNAS, 117(16), 9122-9126. https://doi.org/10.1073/pnas.2004064117.
    11. Prem, K., Liu, Y., Russell, T. W., et al. (2020). "The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic." The Lancet Public Health, 5(5), e261-e270. https://doi.org/10.1016/S2468-2667(20)30073-6.
    12. Cori, A., Ferguson, N. M., Fraser, C., & Cauchemez, S. (2013). "A new framework and software to estimate time-varying reproduction numbers during epidemics." American Journal of Epidemiology, 178(9), 1505-1512. https://doi.org/10.1093/aje/kwt133.
    13. Flaxman, S., Mishra, S., Gandy, A., et al. (2020). "Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe." Nature, 584(7820), 257-261.
    14. Funk, S., Salathe, M., & Jansen, V. A. (2010). "Modelling the influence of human behaviour on the spread of infectious diseases." Journal of the Royal Society Interface, 7(50), 1247-1256. https://doi.org/10.1098/rsif.2010.0142.
    15. Sattenspiel, L., & Dietz, K. (1995). "A structured epidemic model incorporating geographic mobility among regions." Mathematical Biosciences, 128(1-2), 71-91. https://doi.org/10.1016/0025-5564(94)00068-B.
    16. Kerr, C. C., Stuart, R. M., Mistry, D., et al. (2021). "Covasim: an agent-based model of COVID-19 dynamics and interventions." PLOS Computa-tional Biology, 17(7), e1009149. https://doi.org/10.1371/journal.pcbi.1009149.
    17. Pastor-Satorras, R., Castellano, C., Van Mieghem, P., & Vespignani, A. (2015). "Epidemic processes in complex networks." Reviews of Modern Physics, 87(3), 925. https://doi.org/10.1103/RevModPhys.87.925.
    18. Dong, E., Du, H., & Gardner, L. (2020). "An interactive web-based dashboard to track COVID-19 in real time." The Lancet Infectious Diseases, 20(5), 533-534. https://doi.org/10.1016/S1473-3099(20)30120-1.
    19. Hasell, J., Mathieu, E., Beltekian, D., et al. (2020). "A cross-country database of COVID-19 testing." Scientific Data, 7(1), 345. https://doi.org/10.1038/s41597-020-00688-8.

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  • How to Cite

    Man‎e, D. T. . ., Wagh , K. S. ., Patil, K. T. . ., Dhope , T. S. ., Mali , N. D. ., Kulkarni, N. S. . ., & Gupta , D. . (2025). Mathematical Modeling of Epidemic Spread: COVID-19 Case ‎Study and Future Pandemic Preparedness. International Journal of Basic and Applied Sciences, 14(3), 88-93. https://doi.org/10.14419/7tx0yh53