zbMATH — the first resource for mathematics

Absorption in stochastic epidemics. (English) Zbl 1165.92319
Summary: 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 the last section are meant to illustrate possible different asymptotics of solutions to the equation.
92D30 Epidemiology
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
Full Text: Link EuDML
[1] L. J. S. Allen and N. Kirupaharan: Asymptotic dynamics of deterministic and stochastic epidemic models with multiple pathogens. Internat. J. Numer. Anal. Modeling 3 (2005), 2, 329-344. · Zbl 1080.34033
[2] A. N. Borodin and P. Salminen: Handbook of Brownian Motion-Facts and Formulae. Birkh\(\ddot{{\mathrm a}}\)user Verlag, Basel - Boston - Berlin 2002. · Zbl 1012.60003
[3] S. Busenberg and C. Kenneth: Vertically Transmitted Diseases - Models and Dynamics. Springer-Verlag, Berlin - Heidelberg - New York 1993. · Zbl 0837.92021
[4] D. J. Daley and J. Gani: Epidemic Modelling: An Introduction. Cambridge University Press, Cambridge 1999. · Zbl 0922.92022
[5] P. Greenwood, L. F. Gordillo, and R. Kuske: Autonomous stochastic resonance produces epidemic oscillations of fluctuating Size. Proc. Prague Stochastics 2006 (M. Hušková and M. Janžura, Matfyzpress, Praha 2006.
[6] N. Ikeda and S. Watanabe: Stochastic Differential Equation and Diffusion Processes. North-Holland, Amsterdam 1981. · Zbl 0495.60005
[7] J. Kalas and Z. Pospíšil: Continuous Models in Biology (in Czech).Masarykova Univerzita v Brně, Brno 2001.
[8] O. Kallenberg: Foundations of Modern Probability. Second edition. Springer, New York 2002. · Zbl 0996.60001
[9] W. O. Kermack and A. G. McKendrick: A contribution to the mathematical theory of epidemics. Proc. Roy. Soc. London A 155 (1927), 700-721. · JFM 53.0517.01
[10] L. C. G. Rogers and D. Williams: Diffusions, Markov Processes and Martingales. Cambridge University Press, Cambridge 2006. · Zbl 0826.60002
[11] J. Štěpán and D. Hlubinka: Kermack-McKendrick epidemic model revisited. Kybernetika 43 (2007), 4, 395-414. · Zbl 1137.37338 · www.kybernetika.cz · eudml:33866
[12] T. Wai-Yuan and W. Hulin: Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention. World Scientific, Singapore 2005. · Zbl 1141.92328 · www.worldscientific.com
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.