Absorption in stochastic epidemics
Kybernetika (2009)
- Volume: 45, Issue: 3, page 458-474
- ISSN: 0023-5954
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topŠtěpán, Josef, and Staněk, Jakub. "Absorption in stochastic epidemics." Kybernetika 45.3 (2009): 458-474. <http://eudml.org/doc/37667>.
@article{Štěpán2009,
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.},
author = {Štěpán, Josef, Staněk, Jakub},
journal = {Kybernetika},
keywords = {SIR epidemic models; stochastic epidemic models; stochastic differential equation; strong solution; weak solution; absorption; Kermack–McKendrick model; SIR epidemic models; stochastic epidemic models; stochastic differential equation; strong solution; weak solution; absorption; Kermack-McKendrick model},
language = {eng},
number = {3},
pages = {458-474},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Absorption in stochastic epidemics},
url = {http://eudml.org/doc/37667},
volume = {45},
year = {2009},
}
TY - JOUR
AU - Štěpán, Josef
AU - Staněk, Jakub
TI - Absorption in stochastic epidemics
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 3
SP - 458
EP - 474
AB - 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.
LA - eng
KW - SIR epidemic models; stochastic epidemic models; stochastic differential equation; strong solution; weak solution; absorption; Kermack–McKendrick model; SIR epidemic models; stochastic epidemic models; stochastic differential equation; strong solution; weak solution; absorption; Kermack-McKendrick model
UR - http://eudml.org/doc/37667
ER -
References
top- Asymptotic dynamics of deterministic and stochastic epidemic models with multiple pathogens, Internat. J. Numer. Anal. Modeling 3 (2005), 2, 329–344. MR2112651
- Handbook of Brownian Motion-Facts and Formulae, Birkhuser Verlag, Basel – Boston – Berlin 2002. MR1912205
- Vertically Transmitted Diseases – Models and Dynamics, Springer-Verlag, Berlin – Heidelberg – New York 1993. MR1206227
- Epidemic Modelling: An Introduction, Cambridge University Press, Cambridge 1999. MR1688203
- Autonomous stochastic resonance produces epidemic oscillations of fluctuating Size, In: Proc. Prague Stochastics 2006 (M. Hušková and M. Janžura, eds.), Matfyzpress, Praha 2006.
- Stochastic Differential Equation and Diffusion Processes, North-Holland, Amsterdam 1981. MR1011252
- [unknown], J. Kalas and Z. Pospíšil: Continuous Models in Biology (in Czech).Masarykova Univerzita v Brně, Brno 2001.
- Foundations of Modern Probability, Second edition. Springer, New York 2002. Zbl0996.60001MR1876169
- A contribution to the mathematical theory of epidemics, Proc. Roy. Soc. London A 155 (1927), 700–721.
- Diffusions, Markov Processes and Martingales, Cambridge University Press, Cambridge 2006.
- Kermack–McKendrick epidemic model revisited, Kybernetika 43 (2007), 4, 395–414. MR2377919
- Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, World Scientific, Singapore 2005. MR2169300
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