This article is cited in 13 papers

Short Communications

Final probabilities for a branching process with interaction of particles and an epidemic process

A. V. Kalinkin

N. E. Bauman Moscow State Technical University

Abstract: The exponential generating function method suggested in [A. V. Kalinkin, Extinction probability of a branching process with interaction of particles, Theory Probab. Appl., 27 (1982), pp. 201–205] and [A. V. Kalinkin, Final probabilities for a branching random process with interaction of particles, Dokl. Akad. Nauk SSSR, 269 (1983), pp. 1309–1312 (in Russian)] to solve the stationary first (backward) Kolmogorov system of differential equations is applied to the Weiss epidemic model and its generalizations. Integral representations for the generating functions of the final probabilities are obtained.

Keywords: epidemic process, branching process with interaction of particles, hyperbolic equation for double generating function, Riemann method, exact solutions.

Received: 25.11.1997

DOI: 10.4213/tvp2177

 English version: Theory of Probability and its Applications, 1999, 43:4, 633–640

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