I'm a high school student and for my math research paper, I've to model and predict spread of an infectious disease (e.g. covid) in a country of my choice. Which math concepts should I know to do this activity? I've heard that I should learn differential equations, but is there anything else that I must know?
Could you also suggest some good books to learn how to do this?
Thank you,
On
Yes, differential equations are at core of it and for finding the parameters, non-linear optimization is a way to go. This makes it easy to jump to a software tool (e.g. Pyomo for Python) and actually solve it. Actually, here you can find a repo where the SIR-model is used and solved.
When you are talking about designing an optimal strategy on how to deal with pandemics, markov decision processes and dynamic programming comes in handy.
Some good mathematical references:
A biologist's guide to mathematical modeling in ecology and evolution, Otto S.P., Troy D., 2007.
Optimal control of a birth and death epidemic process, Lefevre C., 1981.
Lectures on mathematical modelling of biological systems, Basting G., 2018.
For pandemic-like modeling, usually logistic functions are the right approach. You can research a bit about them here (Wikipedia page). The are those "s" form curves(they are called sigmoid curves if I'm not wrong), and they are useful not only in pandemic but in lots of fields of study.
Some real functional analysis might be enough for you to understand this (derivatives, etc.), and maybe some differential equations.