Example: the SIR epidemic model

Splitting a population into Susceptible, Infected and Recovered and modelling the flow between them.

The SIR model predicts the spread of an infectious disease. The population is divided into three compartments — Susceptible (S), Infected (I) and Recovered (R) — and differential equations describe how people move between them over time.

\frac{d S}{d t} \frac{d I}{d t} \frac{d R}{d t} = - β \frac{S I}{N} = β \frac{S I}{N} - γ I = γ I

Example from the lecture: a flu outbreak in a town of $N = 1000$ people, starting from $S = 990$ , $I = 10$ , $R = 0$ , with transmission rate $β = 0.3$ and recovery rate $γ = 0.1$ .

Solving the equations numerically shows the infected population rising to a peak, then falling as most people recover or gain immunity. The model helps estimate infection peaks and how much interventions like vaccination help.

Formula to remember

Dataset

D = {(x_{i}, y_{i})}_{i = 1}^{n}

A supervised dataset: n examples, each a feature vector with its label.

Quick check · +5 XP

Which of these is a hyperparameter?

Your notes

Saved in this browser as you type.