Seasonal Epidemic Oscillations

SIRS model with seasonal forcing β(t) = β₀(1 + ε·cos(2πt/T))

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SIRS + Forcing: dS/dt = σR − β(t)SI, dI/dt = β(t)SI − γI, dR/dt = γI − σR. Seasonal forcing can drive resonance oscillations, period-doubling, and chaos. Poincaré section (right) shows stroboscopic sampling at each forcing period — fixed point = periodic, cloud = chaos.