Applied mathematics and modelling · Maths EE idea · Solid

What the SIR model predicts about epidemics

A research question to start from

How does the basic reproduction number determine whether an epidemic grows in the SIR model, and what fraction of the population is eventually infected?

A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.

Why it works as a maths EE

A system of differential equations with an exact final-size relation you can derive.

Mathematics you would need

Systems of differential equations
Equilibria and stability
Euler's method
The final-size equation

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Derive the threshold condition.
Derive the final-size relation and solve it numerically.
Discuss assumptions and how changing them alters predictions.

Scope and difficulty

Solid. Solid; keep it theoretical rather than fitting real outbreaks.

Pitfalls

Health essay with copied graphs.
Numerical solutions without analysis.

Where to start reading

Search a library catalogue or a university's open lecture notes for: SIR model final size equation derivation; basic reproduction number threshold. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

Plan this EEOpens the free EE planner with this question as a starting point. Sharpen the questionSix quick checks for a focused research question. Self-check a draftCheck a section against each criterion, free.