Geodesic
Kermack-McKendrick epidemic model revisited
Kybernetika, Tome 43 (2007) no. 4, pp. 395-414.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 34F05, 37N25, 60H10, 60H35, 92D25
Keywords: SIR epidemic models; stochastic differential equations; weak solution; simulation 
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     author = {\v{S}t\v{e}p\'an, Josef and Hlubinka, Daniel},
     title = {Kermack-McKendrick epidemic model revisited},
     journal = {Kybernetika},
     pages = {395--414},
     publisher = {mathdoc},
     volume = {43},
     number = {4},
     year = {2007},
     mrnumber = {2377919},
     zbl = {1137.37338},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_4_a1/}
}
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Štěpán, Josef; Hlubinka, Daniel. Kermack-McKendrick epidemic model revisited. Kybernetika, Tome 43 (2007) no. 4, pp. 395-414. http://geodesic.mathdoc.fr/item/KYB_2007__43_4_a1/