Math

Epidemic: SIR on a network

Compare an SIR compartment model with stochastic infection and recovery on a contact network. Explore transmission, recovery, initial immunity and variability between runs.

By Mykhailo Makarov

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Compare homogeneous SIR equations with random transmission on a fixed contact graph. Rates use days; network outcomes vary with the seed. This is a teaching model, not an epidemic forecast.

Equations used in the module

Equations
S′ = −βSI; I′ = βSI − γI; R′ = γI
S + I + R = 1; Re = βS/γ
Network events: exponential waiting time with total hazard
Susceptible hazard = β × infected neighbours / mean degree

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