Multiregional SIR Model with Infection during Transportation

Diana H Knipl, Gergely Röst

Abstract


We present a general epidemic model to describe the spread of an infectious disease in several regions connected by transportation. We take into account that infected individuals not only carry the disease to a new place while traveling from one region to another, but transmit the disease during travel as well. We obtain that a model structured by travel time is equivalent to a large system of differential equations with multiple delays. By showing the local Lipschitz property of the dynamically defined delayed feedback function, we obtain existence and uniqueness of solutions of the system.

Keywords


epidemic spread; transportation model; dynamically defined delay; Lipschitz continuity

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DOI: http://dx.doi.org/10.11145/j.biomath.2012.09.255

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ISSN 1314-7218 (online)
ISSN 1314-684X (print)

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