External forcing of ecological and epidemiological systems: a resonance approach

Analysing ecological and epidemiological models is complicated by the multiplicity of states that can be excited in the interaction between model nonlinearity and external forcing. This multiplicity, typically created by a hierarchy of subcritical subharmonics, can lead to high amplification of the forcing signal and complex switching under chaos and stochastic externalities. Our objective is to understand the structure of these possible modes of system oscillation, in particular the conditions under which they appear and disappear. The analysis is carried out by transforming the problem into a problem of locating the resonances of the system under variable period forcing. The hierarchy of resonances identified has a well defined generic structure based on the natural period of oscillation of the model, whether stable or unstable when isolated. The usefulness and simplicity of this approach is illustrated in a discussion of a range of human diseases.