Geodesic
Final probabilities for a~branching process with interaction of~particles and an~epidemic process
Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 4, pp. 773-780

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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
Mots-clés : exact solutions. 
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     author = {A. V. Kalinkin},
     title = {Final probabilities for a~branching process with interaction of~particles and an~epidemic process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {773--780},
     publisher = {mathdoc},
     volume = {43},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1998_43_4_a9/}
}
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A. V. Kalinkin. Final probabilities for a~branching process with interaction of~particles and an~epidemic process. Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 4, pp. 773-780. http://geodesic.mathdoc.fr/item/TVP_1998_43_4_a9/