SIR Epidemic Model

anypinn create my-project --template sir

Classic S→I→R compartmental model. Recovers transmission rate \(\beta\) from partially observed infected counts.

Background

The SIR model, introduced by Kermack and McKendrick (1927), is the foundation of compartmental epidemiology. It divides a population into three mutually exclusive compartments — Susceptible, Infected, and Recovered, tracking how individuals flow between them. The dynamics are governed by two competing processes: infection at rate \(\beta\) and recovery at rate \(\delta\), whose ratio defines the basic reproduction number \(R_0 = \beta / \delta\). An epidemic occurs when \(R_0 > 1\).

Governing Equations

\[ \begin{cases} \dfrac{dS}{dt} = -\beta \dfrac{SI}{N} \\[8pt] \dfrac{dI}{dt} = \beta \dfrac{SI}{N} - \delta\, I \end{cases} \]

where:

• \(S(t)\): susceptible population
• \(I(t)\): infected population
• \(N\): total population (constant)
• \(\beta\): transmission rate (to recover)
• \(\delta\): recovery rate (known)

The recovered compartment follows by conservation: \(R(t) = N - S(t) - I(t)\).

Default Configuration

The generated template uses the following values.

Parameters to recover:

Symbol	Code constant	True value
\(\beta\)	TRUE_BETA	\(0.6\)

Known constants:

Symbol	Code constant	Value
\(\delta\)	DELTA	\(1/5 = 0.2\)
\(N\)	N_POP	\(56 \times 10^6\)

Initial conditions: \(S(0) = N - 1, \quad I(0) = 1\)

Domain: \(t \in [0, 90]\) days

Scaling: populations are divided by \(C = 10^6\) and time is normalized by \(T = 90\) in the training ODE. The generated code maps between physical and scaled units automatically.

Features Demonstrated

• Scalar Parameter recovery
• ValidationRegistry for ground-truth comparison
• DataScaling callback for population-scale normalization

Results