6.2.1 Empirically Driven and Mechanistic Models

• Mechanistic, e.g., the SIR model (Susceptible, Infectious, Recovered), also known as a compartmental model.
• Based on explicit equations and known relationships between variables.

Differential equations for the SIR model:

$$\begin{cases} \frac{dS}{dt}=-\beta \frac{I}{N}S\\\\ \frac{dI}{dt}=\beta \frac{I}{N}S - \gamma I \\\\ \frac{dR}{dt}=\gamma I \end{cases}$$

$\beta$: infectiousness

$N$: population size ($S + I + R$)

$\gamma$: recovery

Analogy of compartmental modelling using flow of water through buckets, KO Roster 2024

From: Introduction to SIR Modelling.