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A multi-city epidemic model


  • Julien Arino
  • P. van den Driessche


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 .

Suggested Citation

  • Julien Arino & P. van den Driessche, 2003. "A multi-city epidemic model," Mathematical Population Studies, Taylor & Francis Journals, vol. 10(3), pages 175-193.
  • Handle: RePEc:taf:mpopst:v:10:y:2003:i:3:p:175-193
    DOI: 10.1080/08898480306720

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    Cited by:

    1. Duijzer, L.E. & van Jaarsveld, W.L. & Wallinga, J. & Dekker, R., 2015. "Dose-optimal vaccine allocation over multiple populations," Econometric Institute Research Papers EI2015-29, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. repec:eee:apmaco:v:294:y:2017:i:c:p:49-76 is not listed on IDEAS
    3. Wang, Jianrong & Liu, Maoxing & Li, Youwen, 2013. "Analysis of epidemic models with demographics in metapopulation networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1621-1630.
    4. Constanza Fosco, 2012. "Spatial Difusion and Commuting Flows," Documentos de Trabajo en Economia y Ciencia Regional 30, Universidad Catolica del Norte, Chile, Department of Economics, revised Sep 2012.
    5. Sharma, Natasha & Gupta, Arvind Kumar, 2017. "Impact of time delay on the dynamics of SEIR epidemic model using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 114-125.

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