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.