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

共 50 条

[1] GENERALIZATION OF THE KERMACK-MCKENDRICK DETERMINISTIC EPIDEMIC MODEL
CAPASSO, V
SERIO, G
MATHEMATICAL BIOSCIENCES, 1978, 42 (1-2) : 43 - 61
[2] The Kermack-McKendrick epidemic model revisited
Brauer, F
MATHEMATICAL BIOSCIENCES, 2005, 198 (02) : 119 - 131
[3] Kermack-McKendrick epidemic model revisited
Stepan, Josef
Hlubinka, Daniel
KYBERNETIKA, 2007, 43 (04) : 395 - 414
[4] An extension of the Kermack-McKendrick model for AIDS epidemic
Huang, XC
Villasana, M
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2005, 342 (04): : 341 - 351
[5] The Kermack-McKendrick epidemic model with variable infectivity modified
Skakauskas, V
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 507 (02)
[6] Traveling waves in the Kermack-McKendrick epidemic model with latent period
He, Junfeng
Tsai, Je-Chiang
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2019, 70 (01):
[7] THE KERMACK-MCKENDRICK EPIDEMIC THRESHOLD THEOREM - DISCUSSION
ANDERSON, RM
BULLETIN OF MATHEMATICAL BIOLOGY, 1991, 53 (1-2) : 3 - 32
[8] STANDARD FORM FOR KERMACK-MCKENDRICK EPIDEMIC EQUATIONS
DEAKIN, MAB
BULLETIN OF MATHEMATICAL BIOLOGY, 1975, 37 (01) : 91 - 95
[9] TRAVELING WAVES IN A NONLOCAL DISPERSAL KERMACK-MCKENDRICK EPIDEMIC MODEL
Yang, Fei-Ying
Li, Yan
Li, Wan-Tong
Wang, Zhi-Cheng
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2013, 18 (07): : 1969 - 1993
[10] An analytical solution for the Kermack-McKendrick model
Carvalho, Alexsandro M.
Goncalves, Sebastian
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2021, 566

← 1 2 3 4 5 →