Stochastic SIS metapopulation models for the spread of disease among species in a fragmented landscape

Abstract

Two stochastic models are derived for a susceptible–infectious–susceptible epidemic spreading through a metapopulation: a continuous time Markov chain (CTMC) model and an Itô stochastic differential equation (SDE) model. The stochastic models are numerically compared. Close agreement suggests that computationally intense CTMC simulations can be approximated by simpler SDE simulations. Differential equations for the moments of the SDE probability distribution are also derived, the steady states are solved numerically using a moment closure technique, and these results are compared to simulations. The moment closure technique only coarsely approximates simulation results. The effect of model parameters on stability of the disease-free equilibrium is also numerically investigated.