Far Eastern Mathematical Journal

To content of the issue


Transition phenomena in mathematical theory of epidemic


G. Sh. Tsitsiashvili, M. A. Osipova

2001, issue 1, Ñ. 58–67


Abstract
A generalization of the threshold Whittle's theorem of mathematical epidemic theory is made for a case when a number of susceptibles infected by an end of an epidemic is near its extremal values. It allows to give qualitative long-term prognosis of epidemic's damage. An algorythm of fast and precise calculation of a distribution of epidemic's damage for small meanings which correspond to short-term prognosis is constructed.

Keywords:

Download the article (PDF-file)

References

[1] N. T. J. Bailey, The Mathematical Theory of Infections Diseases, Griffin, London, 1975.
[2] P. Whittle, “The Outcome of a Stochastic Epidemic – a Note on Bailey's Paper”, Biometrika, 42 (1955), 116–122.
[3] A. D. Barbour, “The Principle of Diffusion of Arbitrary Constants”, J. Appl. Probab., 9 (1972), 519–541.
[4] H. E. Daniels, “The Distribution of the Total Size of an Epidemic”, Fifth Berkeley Symp. Math. Statist., Probab., v. 4, Univ. California Press, Berkeley, 1967, 281–283.
[5] G. Reinert, “The Asimptotic Evolution of the General Stochastic Epidemic”, Ann. Appl. Probab., 5 (1995), 1061–1086.
[6] M. S. Bartlett, Stochastic Population Models in Ecology and Epidemiology, Methnen, London, 1960.
[7] G. Sh. Tsitsiashvili, “Transformation of an epidemic model to a random walk and its management”, Math. Scientist, 20 (1995), 103–106.
[8] D. Shtojyan, Kachestvennye svojstva i ocenki stoxasticheskix modelej, Mir, M., 1979, 268 s.
[9] A. N. Shiryaev, Veroyatnost', Nauka, M., 1989, 640 s.

To content of the issue