SEIR Epidemic Model

anypinn create my-project --template seir

Extended epidemic model with an exposed compartment \(E\). Recovers transmission rate \(\beta\) from partially observed data.

Background

The SEIR model extends the classical SIR framework by introducing an Exposed compartment for individuals who are infected but not yet infectious, capturing the incubation period characteristic of diseases such as COVID-19, measles, and influenza. The latency rate \(\sigma\) (inverse of the mean incubation period) controls the transition from exposed to infectious, adding a delay that significantly affects outbreak timing and peak height.

Governing Equations

The model uses population fractions (\(S + E + I + R = 1\)):

\[ \begin{cases} \dfrac{dS}{dt} = -\beta\, S\, I \\[8pt] \dfrac{dE}{dt} = \beta\, S\, I - \sigma\, E \\[8pt] \dfrac{dI}{dt} = \sigma\, E - \gamma\, I \end{cases} \]

where:

• \(S(t)\): susceptible fraction
• \(E(t)\): exposed (latent) fraction
• \(I(t)\): infected fraction
• \(\beta\): transmission rate (to recover)
• \(\sigma\): latency rate, i.e. \(1 / \text{incubation period}\) (known)
• \(\gamma\): recovery rate, i.e. \(1 / \text{infectious period}\) (known)

The recovered fraction follows by conservation: \(R(t) = 1 - S(t) - E(t) - I(t)\).

Default Configuration

The generated template uses the following values.

Parameters to recover:

Symbol	Code constant	True value
\(\beta\)	TRUE_BETA	\(0.5\)

Known constants:

Symbol	Code constant	Value
\(\sigma\)	TRUE_SIGMA	\(1/5.2 \approx 0.192\)
\(\gamma\)	TRUE_GAMMA	\(1/10 = 0.1\)

Initial conditions: \(S(0) = 0.99, \quad E(0) = 0.01, \quad I(0) = 0.001\)

Domain: \(t \in [0, 160]\) days

Features Demonstrated

• Multi-field ODE system (3 fields)
• Scalar Parameter recovery
• ValidationRegistry for ground-truth comparison

Results