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Mathematical Models and Their Applications in Understanding the Dynamics of Infectious Diseases

Author

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  • Shekhar Pokhrel
  • Nikita Sharma
  • Roshan Raj Bahadur Singh Thakuri

Abstract

Infectious diseases pose a persistent global challenge due to their complex transmission dynamics influenced by pathogen evolution, contact patterns, and host interactions. This study reviews how mathematical models have been developed to represent and predict disease spread using differential equations and network frameworks. Compartmental models such as SIS, SIR, SEIR, and SEIATR describe temporal changes in susceptible, infected, and recovered populations, whereas network-based models—including contact, trade, and spatial networks—capture real-world heterogeneity and transmission structure. By analyzing previous modeling studies on diseases such as COVID-19, avian influenza, and African swine fever, this paper demonstrates how mathematical modeling aids in forecasting outbreaks, optimizing control interventions, and guiding public health policies. The findings highlight the need for interdisciplinary collaboration between mathematicians, epidemiologists, and veterinarians to enhance preparedness for emerging infectious diseases.

Suggested Citation

  • Shekhar Pokhrel & Nikita Sharma & Roshan Raj Bahadur Singh Thakuri, 2026. "Mathematical Models and Their Applications in Understanding the Dynamics of Infectious Diseases," Journal of Applied Mathematics, Hindawi, vol. 2026, pages 1-6, February.
    • Handle: RePEc:hin:jnljam:3007179
    DOI: 10.1155/jama/3007179
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