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Kybernetika 45(3):458-474, 2009.

Absorption in Stochastic Epidemics

Josef Štěpán and Jakub Staněk


Abstract:

A two dimensional stochastic differential equation is suggested as a stochastic model for the Kermack--McKendrick epidemics. Its strong (weak) existence and uniqueness and absorption properties are investigated. The examples presented in Section 5 are meant to illustrate possible different asymptotics of a solution to the equation.


Keywords: SIR epidemic models; stochastic epidemic models; stochastic differential equation; strong solution; weak solution; absorption; Kermack--McKendrick model;


AMS: 92D25; 37N25;


full-text.pdf available from August 2009
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BIB TeX

@article{kyb:2009:3:458-474,

author = {\v{S}t\v{e}p\'{a}n, Josef and Stan\v{e}k, Jakub },

title = {Absorption in Stochastic Epidemics},

journal = {Kybernetika},

volume = {45},

year = {2009},

number = {3},

pages = {458-474}

publisher = {{\'U}TIA, AV {\v C}R, Prague },

}


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