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A MULTI-CITY EPIDEMIC MODEL Julien Arino
 

Summary: A MULTI-CITY EPIDEMIC MODEL
Julien Arino
P. van den Driessche
Abstract
Some analytical results are given for a model that describes the prop-
agation of a disease in a population of individuals who travel between n
cities. The model is formulated as a system of 2n2
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 outgo-
ing (or return) travel. An explicit formula that can be used to compute
the basic reproduction number R0 is obtained, and explicit bounds on
R0 are determined in the case of homogeneous contacts between individ-
uals within each city. Numerical simulations indicate that R0 is a sharp
threshold, with the disease dying out if R0 < 1 and reaching an endemic
level in all connected cities if R0 > 1.
INTRODUCTION
The spatial spread of infectious diseases is a phenomenon that involves many
different components. Modeling this spread is a complex task. Spatial hetero-

  

Source: Arino, Julien - Department of Mathematics, University of Manitoba

 

Collections: Mathematics