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A multi-city epidemic model

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  • Julien Arino
  • P. van den Driessche
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    Abstract

    Some analytical results are given for a model that describes the propagation of a disease in a population of individuals who travel between n cities. The model is formulated as a system of 2n 2 ordinary differential equations, with terms accounting for disease transmission, recovery, birth, death, and travel between cities. The mobility component is represented as a directed graph with cities as vertices and arcs determined by outgoing (or return) travel. An explicit formula that can be used to compute the basic reproduction number, {\cal R}_0 , is obtained, and explicit bounds on {\cal R}_0 are determined in the case of homogeneous contacts between individuals within each city. Numerical simulations indicate that {\cal R}_0 is a sharp threshold, with the disease dying out if {\cal R}_0 1 .

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Mathematical Population Studies.

    Volume (Year): 10 (2003)
    Issue (Month): 3 ()
    Pages: 175-193

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    Handle: RePEc:taf:mpopst:v:10:y:2003:i:3:p:175-193

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    Cited by:
    1. Wang, Jianrong & Liu, Maoxing & Li, Youwen, 2013. "Analysis of epidemic models with demographics in metapopulation networks," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 392(7), pages 1621-1630.
    2. Constanza Fosco, 2012. "Spatial Diffusion and Commuting Flows," Documentos de Trabajo en Economia y Ciencia Regional, Universidad Catolica del Norte, Chile, Department of Economics 30, Universidad Catolica del Norte, Chile, Department of Economics, revised Sep 2012.

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