Harmonic resonance

Gist

Definition

When the natural period of osccilations in an Model - SIR is the same as the Seasonal forcing

Forcing is

For example, when R0 is large and the level of seasonal forcing is small, the fraction of infecteds shows harmonic oscillations with small-amplitude annual epidemics (Figure 5.6, top left). As β1 increases to 0.1, we observe subharmonic resonance (as ω ≈ 2F) giving rise to biennial dynamics (Figure 5.6, middle left). A further increase in β1 gives rise to four-year cycles that have a noticeable and pronounced biennial as well as annual component (Figure 5.6, bottom left).