SIRS Model — Seasonal Forcing

The SIRS model extends SIR by allowing recovered individuals to lose immunity and return to susceptible. With seasonal forcing in the transmission rate β(t) = β₀(1 + ε·sin(2πt/T)), the system can exhibit periodic outbreaks, quasi-periodicity, and chaos.

Susceptible

Infectious

Recovered

Parameters

Base β₀ 0.5 Forcing ε 0.3 Recovery γ 0.1 Waning σ 0.05 Season T (yrs) 1.0

Phase portrait: S vs I