Bulletin of Mathematical Biology

, Volume 75, Issue 7, pp 1157–1180

Probability of a Disease Outbreak in Stochastic Multipatch Epidemic Models

Original Article

DOI: 10.1007/s11538-013-9848-z

Cite this article as:
Lahodny, G.E. & Allen, L.J.S. Bull Math Biol (2013) 75: 1157. doi:10.1007/s11538-013-9848-z


Environmental heterogeneity, spatial connectivity, and movement of individuals play important roles in the spread of infectious diseases. To account for environmental differences that impact disease transmission, the spatial region is divided into patches according to risk of infection. A system of ordinary differential equations modeling spatial spread of disease among multiple patches is used to formulate two new stochastic models, a continuous-time Markov chain, and a system of stochastic differential equations. An estimate for the probability of disease extinction is computed by approximating the Markov chain model with a multitype branching process. Numerical examples illustrate some differences between the stochastic models and the deterministic model, important for prevention of disease outbreaks that depend on the location of infectious individuals, the risk of infection, and the movement of individuals.


Multiple patchesInfectious diseasesMultitype branching processMarkov chain

Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA