Seasonal Epidemic Oscillations

Seasonally-forced SIR model · resonance, period-doubling, chaos

5.0
0.20
0.20
0.020
dS/dt = μ − β(t)SI/N − μS  |  dI/dt = β(t)SI/N − (γ+μ)I  |  β(t) = β₀[1 + ε·cos(2πt/T)]
R₀ = 5.0 | Year 0 | I = 0.000 | Peak: —
Seasonal forcing of transmission rate β creates complex epidemic dynamics. Near resonance (R₀ ~ 5–17), annual forcing produces biennial outbreaks. Higher forcing or R₀ can lead to period-doubling cascades and chaos — explaining irregular measles and flu cycles. Bifurcation structure is a classic of nonlinear dynamics.