岡山大学環境理工学部研究報告 ISSN 2187-6940

Published by Faculty of Environmental Science and Technology, Okayama University

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DOI : http://doi.org/10.18926/fest/48237

Basic Reproductive Ratio for Epdiemic Models (Review)

Sumita, Masanori

Kajiwara, Tsuyoshi Kaken ID publons researchmap

fest_017_001_006.pdf 439 KB

Published Date

2012-03

Abstract

We review some fundamental results on the basic reproductive ratio of models in epidemiology following several documents. We present the general denition of the basic reproductive ratio and the threshold theorem of for the stability of the disease free equilibrium. All results for non-negative matrices and non singular M-matrices which we need in the denition of the basic reproductive ratio and the proof of the threshold theorem are also presented. All parts of the review are self-contained, and all parts of the proof are given explicitly.

Keywords

Basic reproductive ratio

epidemic model

Non negative matrix

M-matrix

Note

研究論文　環境数理工学科

ISSN

2185-3347

NCID

AN10529213

NAID

120004025482

JaLCDOI

10.18926/fest/48237