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} }

Powered by bibtexbrowser