Journal
JOURNAL OF MATHEMATICAL BIOLOGY
Volume 60, Issue 5, Pages 645-686Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-009-0280-9
Keywords
Infectious disease; SIR model; Latent period; Patch; Non-local infection; Dispersal; Basic reproduction number
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Funding
- NSERC
- NCE-MITACS of Canada
- PREA of Ontario
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In this paper, with the assumptions that an infectious disease in a population has a fixed latent period and the latent individuals of the population may disperse, we formulate an SIR model with a simple demographic structure for the population living in an n-patch environment (cities, towns, or countries, etc.). The model is given by a system of delay differential equations with a fixed delay accounting for the latency and a non-local term caused by the mobility of the individuals during the latent period. Assuming irreducibility of the travel matrices of the infection related classes, an expression for the basic reproduction number R-0 is derived, and it is shown that the disease free equilibrium is globally asymptotically stable if R-0 < 1, and becomes unstable if R-0 > 1. In the latter case, there is at least one endemic equilibrium and the disease will be uniformly persistent. When n = 2, two special cases allowing reducible travel matrices are considered to illustrate joint impact of the disease latency and population mobility on the disease dynamics. In addition to the existence of the disease free equilibrium and interior endemic equilibrium, the existence of a boundary equilibrium and its stability are discussed for these two special cases.
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