Stochastically Sustained Oscillations: Applications in Ecology and
Epidemiology
Richard Jordan
Mount Holyoke College
Department of Mathematics and Statistics
email: rjordan @mtholyoke.edu
Abstract: Many deterministic (ODE) models in ecology and
epidemiology exhibit asymptotically stable equilibria that are approached via
damped oscillations. Real ecological and epidemiological time series, however,
often display persistent, non-decaying "periodic" oscillations about an
equilibrium point. In this talk, we will demonstrate how incorporating
stochasticity into such a model, either by reformulating it at the microscopic
level as a Markov jump process, or at the macroscopic level as a system of
stochastic differential equations, can lead to sustained oscillations via the
so-called "coherence resonance effect". As a specific example, we will
consider stochastic models of cholera and influenza.