Kermack-McKendrick epidemic model revisited

Štěpán, Josef   ; Hlubinka, Daniel

Kybernetika, Tome 43 (2007) no. 4, pp. 395-414

Abstract (VO)

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.

Détail

Classification : 34F05, 37N25, 60H10, 60H35, 92D25
Keywords: SIR epidemic models; stochastic differential equations; weak solution; simulation

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