A multi-city epidemic model (bibtex)
by J. Arino, P. van den Driessche
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, lcub\cal Rrcub\_0 , is obtained, and explicit bounds on lcub\cal Rrcub\_0 are determined in the case of homogeneous contacts between individuals within each city. Numerical simulations indicate that lcub\cal Rrcub\_0 is a sharp threshold, with the disease dying out if lcub\cal Rrcub\_0 1 .
Reference:
A multi-city epidemic model (J. Arino, P. van den Driessche), In Mathematical Population Studies, volume 10, 2003.
Bibtex Entry:
@Article{ArinoVdD2003a,
  Title                    = {{A multi-city epidemic model}},
  Author                   = {Arino, J. and van den Driessche, P.},
  Journal                  = {Mathematical Population Studies},
  Year                     = {2003},
  Number                   = {3},
  Pages                    = {175--193},
  Volume                   = {10},

  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, lcub\cal Rrcub\_0 , is obtained, and explicit bounds on lcub\cal Rrcub\_0 are determined in the case of homogeneous contacts between individuals within each city. Numerical simulations indicate that lcub\cal Rrcub\_0 is a sharp threshold, with the disease dying out if lcub\cal Rrcub\_0 1 .},
  Doi                      = {10.1080/08898480306720},
  Url                      = {http://server.math.umanitoba.ca/~jarino/papers/ArinoVdD-2003-MPS10.correct.pdf}
}
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