Mathematical Epidemiology and the SIR System: How We Can Reduce the Spread of Infectious Diseases

During Fall Term in the 2025-26 academic year, I combined epidemiology, virology, and mathematics to model past and predict future influenza seasons in New York State. Every year, roughly in October through May, we experience the flu season, and I wanted to bring awareness to the prediction and planning that goes into having accurate influenza data available to the public. With data from the NYS Department of Health and MATLAB, I used the SIR system (Susceptible, Infected, Removed) of ordinary differential equations to model the 2018-19, 2020-21, and 2022-23 New York State flu seasons. I used these models to write a modified code that predicted the 2025-26 flu season. This model helps simulate how a contagious disease spreads and eventually declines in a population over time. In addition to building these flu models, I looked at the different methods of how flu season data is collected, as well as some ethical concerns that come with the data collections. Finally, I looked at some of the limitations that come with mathematical modeling, and what improvements I could make to the models and data collection. Modeling flu seasons is an important part of public health preparedness as it helps with vaccine timing, outbreak response, and hospital readiness.