The Asymptotic Analysis of a Stochastic Model of an Epidemic

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Previous article Next article The Asymptotic Analysis of a Stochastic Model of an EpidemicA. V. Nagaev and A. N. StartsevA. V. Nagaev and A. N. Startsevhttps://doi.org/10.1137/1115007PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Norman T. J. Bailey, The mathematical theory of epidemics, Hafner Publishing Co., New York, 1957viii+194 MR0095085 Google Scholar[2] F. G. Foster, A note on Bailey's and Whittle's treatment of a general stochastic epidemic, Biometrika, 42 (1955), 123–125 MR0070100 0064.39201 Google Scholar[3] V. Siskind, A solution of the general stochastic epidemic, Biometrika, 52 (1965), 613–616 MR0207409 0134.37909 CrossrefGoogle Scholar[4] I. I. Gikhman and , A. V. Skorokhod, Introduction to the theory of random processes, Translated from the Russian by Scripta Technica, Inc, W. B. Saunders Co., Philadelphia, Pa., 1969xiii+516 MR0247660 Google Scholar[5] A. V. Skorokhod, Random Processes with Independent Increments, Izd-vo “Nauka”, Moskva, 1964, (In Russian.) Google Scholar[6] A. V. Nagaev and , A. V. Starcev, A threshold theorem for a certain model of an epidemic, Mat. Zametki, 3 (1968), 179–185, (In Russian.) MR0229324 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Hybrid Markov chain models of S–I–R disease dynamics24 December 2016 | Journal of Mathematical Biology, Vol. 75, No. 3 Cross Ref Diffusion Models in Life Sciences24 August 2012 Cross Ref Applications of branching processes to the final size of SIR epidemics22 January 2010 Cross Ref On a Model of Interacting Particles of Two Types Generalizing the Bartlett--McKendrick Epidemic ProcessA. N. Startsev25 July 2006 | Theory of Probability & Its Applications, Vol. 46, No. 3AbstractPDF (207 KB)Asymptotic analysis of the general stochastic epidemic with variable infectious periods14 July 2016 | Journal of Applied Probability, Vol. 38, No. 01 Cross Ref Asymptotic analysis of the general stochastic epidemic with variable infectious periods14 July 2016 | Journal of Applied Probability, Vol. 38, No. 1 Cross Ref On the Distribution of the Size of an Epidemicin a Non-Markovian ModelA. N. Startsev25 July 2006 | Theory of Probability & Its Applications, Vol. 41, No. 4AbstractPDF (245 KB)On a Daley-Kendall model of random rumours14 July 2016 | Journal of Applied Probability, Vol. 27, No. 1 Cross Ref The transitive closure of a random digraphRandom Structures and Algorithms, Vol. 1, No. 1 Cross Ref Extreme values of Markov population processesStochastic Processes and their Applications, Vol. 14, No. 3 Cross Ref Journal of Applied Probability, Vol. 20, No. 2 Cross Ref Brownian motion and a sharply curved boundary1 July 2016 | Advances in Applied Probability, Vol. 13, No. 4 Cross Ref An application of a martingale central limit theorem to the standard epidemic modelStochastic Processes and their Applications, Vol. 11, No. 1 Cross Ref Threshold limit theorems for some epidemic processes1 July 2016 | Advances in Applied Probability, Vol. 12, No. 2 Cross Ref A useful random time-scale transformation for the standard epidemic model14 July 2016 | Journal of Applied Probability, Vol. 17, No. 2 Cross Ref CENTRAL LIMIT ANALOGUES FOR MARKOV POPULATION PROCESSES Cross Ref Gaussian approximation of some closed stochastic epidemic models14 July 2016 | Journal of Applied Probability, Vol. 14, No. 2 Cross Ref A Limit Distribution of the Duration of an EpidemicA. V. Nagaev and T. P. Mukhomor17 July 2006 | Theory of Probability & Its Applications, Vol. 20, No. 4AbstractPDF (814 KB)Quasi–stationary distributions in Markov population processes1 July 2016 | Advances in Applied Probability, Vol. 8, No. 2 Cross Ref Limit theorems and diffusion approximations for density dependent Markov chains23 February 2009 Cross Ref The maximum size of a closed epidemic1 July 2016 | Advances in Applied Probability, Vol. 6, No. 4 Cross Ref Some approximate solutions to the discrete master equationJournal of Statistical Physics, Vol. 6, No. 2-3 Cross Ref Representation and approximation of counting processes Cross Ref Volume 15, Issue 1| 1970Theory of Probability & Its Applications History Submitted:26 April 1968Published online:17 February 2012 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1115007Article page range:pp. 98-107ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics