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Sib. Èlektron. Mat. Izv., 2017, Volume 14, Pages 1413–1423 (Mi semr879)  

Differentical equations, dynamical systems and optimal control

On group properties of epidemics equation

A. V. Mastikhin

Bauman Moscow State Technical University, ul. Baumanskaya 2-ya, 5/1, 105005, Moscow, Russia

Abstract: 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.

DOI: https://doi.org/10.17377/semi.2017.14.120

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Bibliographic databases:

UDC: 517.9
MSC: 60J27
Received April 18, 2017, published December 12, 2017

Citation: A. V. Mastikhin, “On group properties of epidemics equation”, Sib. Èlektron. Mat. Izv., 14 (2017), 1413–1423

Citation in format AMSBIB
\Bibitem{Mas17}
\by A.~V.~Mastikhin
\paper On group properties of epidemics equation
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 1413--1423
\mathnet{http://mi.mathnet.ru/semr879}
\crossref{https://doi.org/10.17377/semi.2017.14.120}


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