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Title: Kermack-McKendrick epidemic model revisited (English)
Author: Štěpán, Josef
Author: Hlubinka, Daniel
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 43
Issue: 4
Year: 2007
Pages: 395-414
Summary lang: English
Category: math
Summary: This paper proposes a stochastic diffusion model for the spread of a susceptible-infective-removed Kermack–McKendric epidemic (M1) in a population which size is a martingale $N_t$ that solves the Engelbert–Schmidt stochastic differential equation (). The model is given by the stochastic differential equation (M2) or equivalently by the ordinary differential equation (M3) whose coefficients depend on the size $N_t$. Theorems on a unique strong and weak existence of the solution to (M2) are proved and computer simulations performed. (English)
Keyword: SIR epidemic models
Keyword: stochastic differential equations
Keyword: weak solution
Keyword: simulation
MSC: 34F05
MSC: 37N25
MSC: 60H10
MSC: 60H35
MSC: 92D25
idZBL: Zbl 1137.37338
idMR: MR2377919
Date available: 2009-09-24T20:24:56Z
Last updated: 2012-06-06
Stable URL:
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