An Adaptation of Deterministic SIR Models: Mathematically Modeling the Spread of Infectious Diseases

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Kris Nairn, Mathematics


Mathematical Biology is a relatively new area of mathematics that involves mathematicians working with biologists. Biologists will typically pose a question while the mathematician will develop a model and simulate that question. Developing mathematical models for aspects of biology can be very difficult because it involves determining a relationship between biological variables and identifying rate parameters. These rate parameters need to be estimated, which can lead to discrepancies in the models. However, even simple models can provide useful information about how a disease spreads, how an ecosystem grows, or how effective a vaccination is on a system. With mathematical biology, mathematics can help advance biology and biology can help inspire mathematics. The particular area of Mathematical Biology that I focused on was Evolutionary Biology. I looked particularly at mathematical epidemiology and how an infectious disease can spread and affect a population. I sought to understand how these mathematical models work and how they could be adapted to be applicable in more situations. I compared the differences between using a deterministic model and a stochastic model. Moreover, creating a probabilistic model and adding randomness can also provide a more realistic view of how a disease spreads.

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