Kermack-McKendrick epidemic model revisited

Josef Štěpán; Daniel Hlubinka

Kybernetika (2007)

  • Volume: 43, Issue: 4, page 395-414
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Štěpán, Josef, and Hlubinka, Daniel. "Kermack-McKendrick epidemic model revisited." Kybernetika 43.4 (2007): 395-414. <http://eudml.org/doc/33866>.

@article{Štěpán2007,
abstract = {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.},
author = {Štěpán, Josef, Hlubinka, Daniel},
journal = {Kybernetika},
keywords = {SIR epidemic models; stochastic differential equations; weak solution; simulation; SIR epidemic models; stochastic differential equations; weak solution; simulation},
language = {eng},
number = {4},
pages = {395-414},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Kermack-McKendrick epidemic model revisited},
url = {http://eudml.org/doc/33866},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Štěpán, Josef
AU - Hlubinka, Daniel
TI - Kermack-McKendrick epidemic model revisited
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 4
SP - 395
EP - 414
AB - 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.
LA - eng
KW - SIR epidemic models; stochastic differential equations; weak solution; simulation; SIR epidemic models; stochastic differential equations; weak solution; simulation
UR - http://eudml.org/doc/33866
ER -

References

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  17. Štěpán J., Dostál P., The d X ( t ) = X b ( X ) d t + X σ ( X ) d W equation and financial mathematics I, Kybernetika 39 (2003), 653–680 MR2035643
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