The SIR epidemic model from a PDE point of view

被引：29
|
作者：
Chalub, Fabio A. C. C. [2 ,3 ]
Souza, Max O. [1 ]
机构：
[1] Univ Fed Fluminense, Dept Matemat Aplicada, BR-22240920 Niteroi, RJ, Brazil
[2] Univ Nova Lisboa, Dept Matemat, P-2829516 Quinta Da Torre, Caparica, Portugal
[3] Univ Nova Lisboa, Ctr Matemat & Aplicacoes, P-2829516 Quinta Da Torre, Caparica, Portugal
来源：
MATHEMATICAL AND COMPUTER MODELLING | 2011年 / 53卷 / 7-8期
关键词：
Epidemiology; Markov chains; Conservation laws; Thermodynamical limit; MATHEMATICAL-THEORY; ENDEMICITY;
D O I：
10.1016/j.mcm.2010.05.036
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
We present a derivation of the classical Susceptible-Infected-Removed (SIR) and Susceptible-Infected-Removed-Susceptible (SIRS) models through a mean-field approximation from a discrete version of SIR(S). We then obtain a hyperbolic forward Kolmogorov equation, and show that its projected characteristics recover the standard SIR(S) model. Moreover, for the SIRS model, we show that the long time limit of the SIRS model will be a Dirac measure supported on the corresponding isolated equilibria. For the SIR model, we show that the long time limit is a Radon measure supported in a segment of nonisolated equilibria. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1568 / 1574
页数：7
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