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1718658 Vol 9 · Issue 11 Download Paper

Understanding Epidemics: How Differential Equations Help Us Fight Disease

Lavkush Pandey

Subject area: Science,Engineering and Technology  ·  Area of research: Mathematics

DOI: 10.64388/IREV9I11-1718658

Abstract

Infectious diseases are part of human history, shaping societies, economies, and daily life. From seasonal influenza to global pandemics such as COVID‑19, predicting how diseases spread and how interventions work is critical. Mathematical tools, particularly differential equations, allow us to observe the underlying dynamics of epidemics: the flow of people between susceptible, infected, and recovered states. This paper explores the application of differential equations in epidemic modeling, discusses classical models like SIR and SEIR, examines real-world examples, and highlights how these models guide public health strategies. The paper also addresses challenges and outlines directions for future research, emphasizing the importance of mathematical modeling in understanding and managing epidemics.

Keywords

Epidemic Modeling, Differential Equations, SIR Model, SEIR Model, Disease Dynamics, Public Health, Infectious Disease Prediction, Mathematical Epidemiology

References

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[2] Rajendrakumar, A. L., Nair, A. T., Nangia, C., Chourasia, P. K., Chourasia, M. K., Syed, M. G., … FazaludeenKoya, M. S. (2020). Epidemic landscape and forecasting of SARS‑CoV‑2 in India. Journal of Epidemiology and Global Health, 11, 55–59.

[3] Yadav, R. S. (2020). Mathematical modeling and simulation of SIR model for COVID‑2019 epidemic outbreak: A case study of India. medRxiv.https://doi.org/10.1101/2020.05.15.20103077

[4] Purkayastha, S., Bhattacharyya, R., Bhaduri, R., Kundu, R., Gu, X., Salvatore, M., … Ray, D. (2021). A comparison of five epidemiological models for transmission of SARS‑CoV‑2 in India. BMC Infectious Diseases, 21, 533.

[5] Sumathi, M., Abilasha, B., Ravikumar, S., &Veeramani, C. (2023). An optimal control of bi‑modal COVID‑19 SEIQR epidemic spreading model in India. Research in Control, 100256.

[6] Bandekar, S. R. (2022). Mathematical modeling of COVID‑19 in India and its states with control strategies. Applied Mathematical Modelling.

[7] Kaur, R. (2026). Mathematical modelling in epidemiology: SIR and seasonal models. Resonance – Journal of Science Education.

[8] Rao, A. S. R. S. (2003). Mathematical modelling of AIDS epidemic in India. Journal of Biological Systems.

[9] Gupta, H. (2021). Data analytics and mathematical modeling for simulating the dynamics of COVID‑19 epidemic—A case study of India. Electronics, 10(2), 127.

[10] Pell, B., Phan, T., Rutter, E. M., Chowell, G., &Kuang, Y. (2018). Simple multi‑scale modeling of the transmission dynamics of the 1905 plague epidemic in Bombay. Mathematical Biosciences, 301, 83–92.

[11] Khanday, M. A., &Zargar, F. (2021). Mathematical analysis on the dynamics of COVID‑19 in India using SIR epidemic model. Mapana Journal of Sciences.

[12] Kushwaha, P. (2025). Mathematical modeling of epidemics using stochastic differential equations: A review. Recent Trends in Mathematics, 01(02), 1–6.

[13] Li, M. Y. (2018). An introduction to mathematical modeling of infectious diseases. Springer.

[14] Okabe, Y., &Shudo, A. (2020). A mathematical model of epidemics: A tutorial for students. Mathematics, 8(7), 1174.

[15] Martcheva, M. (2015). An introduction to mathematical epidemiology. Springer.

[16] Behl, R., & Mishra, M. (2020). COVID‑19 lifecycle: Predictive modelling of states in India. Indian Journal of Statistics & Decision, 21(4).

[17] Ross, R., Mc Kendrick, A. G., & Kermack, W. O. (1927/1991). A contribution to the mathematical theory of epidemics. Bulletin of Mathematical Biology. Republished classic foundational work.

How to cite this paper

Lavkush Pandey "Understanding Epidemics: How Differential Equations Help Us Fight Disease" Iconic Research And Engineering Journals Volume 9 Issue 11 2026 Page 5166-5170 https://doi.org/10.64388/IREV9I11-1718658
Lavkush Pandey "Understanding Epidemics: How Differential Equations Help Us Fight Disease" Iconic Research And Engineering Journals, vol. 9, no. 11, May. 2026, doi: https://doi.org/10.64388/IREV9I11-1718658
Lavkush Pandey (2026). Understanding Epidemics: How Differential Equations Help Us Fight Disease. Iconic Research And Engineering Journals, 9(11). doi: https://doi.org/10.64388/IREV9I11-1718658
Lavkush Pandey "Understanding Epidemics: How Differential Equations Help Us Fight Disease" Iconic Research And Engineering Journals, vol. 9, no. 11, May. 2026. Crossref, https://doi.org/10.64388/IREV9I11-1718658
@article{1718658,
      author = {Lavkush Pandey},
      title = {Understanding Epidemics: How Differential Equations Help Us Fight Disease},
      journal = {Iconic Research And Engineering Journals},
      year = {2026},
      volume = {9},
      number = {11},
      pages = {5166-5170},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1718658.pdf},
      abstract = {Infectious diseases are part of human history, shaping societies, economies, and daily life. From seasonal influenza to global pandemics such as COVID‑19, predicting how diseases spread and how interventions work is critical. Mathematical tools, particularly differential equations, allow us to observe the underlying dynamics of epidemics: the flow of people between susceptible, infected, and recovered states. This paper explores the application of differential equations in epidemic modeling, discusses classical models like SIR and SEIR, examines real-world examples, and highlights how these models guide public health strategies. The paper also addresses challenges and outlines directions for future research, emphasizing the importance of mathematical modeling in understanding and managing epidemics.},
      keywords = {Epidemic Modeling, Differential Equations, SIR Model, SEIR Model, Disease Dynamics, Public Health, Infectious Disease Prediction, Mathematical Epidemiology},
      month = {May},
      doi = {https://doi.org/10.64388/IREV9I11-1718658}
  }