A graph-theoretic method for the basic reproduction number in continuous time epidemiological models期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A graph-theoretic method for the basic reproduction number in continuous time epidemiological models

Authors:	Tomás de-Camino-Beck Mark A. Lewis P. van den Driessche

Affiliation:	(1) Department of Mathematical and Statistical Sciences, Centre for Mathematical Biology, University of Alberta, Edmonton, AB, T6G 2G1, Canada;(2) Present address: Department of Entomology, Penn State University, ASI Bldg, State College, PA 16802, USA;(3) Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada

Abstract:	In epidemiological models of infectious diseases the basic reproduction number ${mathcal{R}_0}$ is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian elimination using digraph reduction is derived and an algorithm given for calculating the basic reproduction number in continuous time epidemiological models. Examples illustrate how this method can be applied to compartmental models of infectious diseases modelled by a system of ordinary differential equations. We also show with these examples how lower bounds for ${mathcal{R}_0}$ can be obtained from the digraphs in the reduction process.

Keywords:	Mathematics Subject Classification (2000) 92D30 05C50
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