THE DETERMINISTIC KERMACK-MCKENDRICK MODEL BOUNDS THE GENERAL STOCHASTIC EPIDEMIC

被引：5

作者：

Wilkinson, Robert R. ^{[1
]}

Ball, Frank G. ^{[2
]}

Sharkey, Kieran J. ^{[1
]}

机构：

[1] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside, England

[2] Univ Nottingham, Sch Math Sci, Univ Pk, Nottingham NG7 2RD, England

来源：

JOURNAL OF APPLIED PROBABILITY | 2016年 / 53卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

General stochastic epidemic; deterministic general epidemic; SIR; Kermack-McKendrick; message passing; bound;

D O I：

10.1017/jpr.2016.62

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove that, for Poisson transmission and recovery processes, the classic susceptible -> infected -> recovered (SIR) epidemic model of Kermack and McKendrick provides, for any given time t > 0, a strict lower bound on the expected number of susceptibles and a strict upper bound on the expected number of recoveries in the general stochastic SIR epidemic. The proof is based on the recent message passing representation of SIR epidemics applied to a complete graph.

引用

页码：1031 / 1040

页数：10

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