Multi-patch deterministic and stochastic models for wildlife diseases

Robert K. McCormack, Linda J.S. Allen

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

Spatial heterogeneity and host demography have a direct impact on the persistence or extinction of a disease. Natural or human-made landscape features such as forests, rivers, roads, and crops are important to the persistence of wildlife diseases. Rabies, hantaviruses, and plague are just a few examples of wildlife diseases where spatial patterns of infection have been observed. We formulate multi-patch deterministic and stochastic epidemic models and use these models to investigate problems related to disease persistence and extinction. We show in some special cases that a unique disease-free equilibrium exists. In these cases, a basic reproduction number ℝ0 can be computed and shown to be bounded below and above by the minimum and maximum patch reproduction numbers ℝj, j=1, …, n. The basic reproduction number has a simple form when there is no movement or when all patches are identical or when the movement rate approaches infinity. Numerical examples of the deterministic and stochastic models illustrate the disease dynamics for different movement rates between three patches.

Original languageEnglish
Pages (from-to)63-85
Number of pages23
JournalJournal of Biological Dynamics
Volume1
Issue number1
DOIs
StatePublished - Jan 2007

Keywords

  • Epidemic models
  • Multiple patches
  • Stochastic models

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