Geodesic
On group properties of epidemics equation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1413-1423

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We consider a time-homogeneous Markov process on discret set of states known as Weiss (simple) epidemic process. For exponential (double) generating function of the transition probabilities we consider system of first and second Kolmogorov equations. The system exact solution was obtained by using Lie group methods. We also discuss the opportunity of using the same method in the case of general epidemic process.
Keywords: Markov process, exponential (double) generating function, first and second Kolmogorov equation, Fourier method, simple epidemic, general epidemic, infinitesimal symmetry generator, Lie algebra. 
@article{SEMR_2017_14_a100,
     author = {A. V. Mastikhin},
     title = {On group properties of epidemics equation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1413--1423},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a100/}
}
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A. V. Mastikhin. On group properties of epidemics equation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1413-1423. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a100/