Geodesic
Absorption in stochastic epidemics
Kybernetika, Tome 45 (2009) no. 3, pp. 458-474.

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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.
Classification : 37N25, 60H10, 92D25, 92D30
Keywords: SIR epidemic models; stochastic epidemic models; stochastic differential equation; strong solution; weak solution; absorption; Kermack–McKendrick model 
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Štěpán, Josef; Staněk, Jakub. Absorption in stochastic epidemics. Kybernetika, Tome 45 (2009) no. 3, pp. 458-474. http://geodesic.mathdoc.fr/item/KYB_2009__45_3_a6/