mirtrМир транспортаWorld of Transport and Transportation1992-3252Russian University of Transport (RUT)10.30932/1992-3252-2020-18-6-06-29mirtr-2051Research ArticleВОПРОСЫ ТЕОРИИTHEORYМатематическая модель распространения эпидемии внутри железнодорожного купейного вагонаMathematical Model of Spread of the Epidemic Inside a Railway Compartment CoachБратусьА. С.BratusA. S.

Братусь Александр Сергеевич – доктор физико-математическихнаук, профессор кафедры математического моделирования и системного анализа Института управления и цифровых технологий

Москва

Bratus, Alexander S. – D.Sc. (Physics and Mathematics), Professor at the Department of Mathematical Modelling and System Analysis of the Institute of Management, Control and Digital Technologies

Moscow

alexander.bratus@yandex.ruОчеретянаяА. С.OcheretyanayaA. S.

Очеретяная Александра Сергеевна – аспирант кафедры математического моделирования и системного анализа Института управления и цифровых технологий

Москва

Ocheretyanaya, Alexandra S. – Ph.D. student at the Department of Mathematical Modelling and System Analysis of the Institute of Management, Control and Digital Technologies

Moscow

sandra.och@yandex.ruРоссийский университет транспортаРоссияRussian University of TransportRussian Federation202028122020186629Copyright © Братусь А.С., Очеретяная А.С., 20202020Братусь А.С., Очеретяная А.С.Bratus A.S., Ocheretyanaya A.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://mirtr.elpub.ru/jour/article/view/2051

В данной статье рассмотрен один из аспектов самой актуальной для 2020 года проблемы – распространения инфекций. В частности, в работе объектом распространения является железнодорожный вагон. Цель – описать распространение эпидемии в железнодорожном вагоне с помощью стохастической модели. Модель вагона представляется в виде сети. Процессы, происходящие на сети, считаются марковскими. В данной работе применено два метода стохастического моделирования: моделирование на основе уравнений Колмогорова и алгоритм Гиллеспи. Уравнения Колмогорова использованы для проверки применимости алгоритма Гиллеспи, который, в свою очередь, использован для расчётов модели вагона. Полученные данные были проанализированы, и на их основе можно сделать заключение о применимости модели на случай типичного пассажирского поезда.

This article discusses an aspect of the most pressing problem of 2020, that of the spread of infectious diseases. The work considers a railway compartment coach as a particular object of spread of infectious diseases. The objective is to describe spread of the epidemic in a railway coach using a stochastic model. The model of the coach is represented as a network. The processes occurring on the network are considered to be Markov processes. In this paper, two methods of stochastic modelling are applied: modelling based on Kolmogorov equations and Gillespie algorithm. Kolmogorov equations are used to test applicability of Gillespie algorithm, which, in turn, is used to simulate the model of the coach. The obtained data were analysed, and based on that analysis it is possible to make a conclusion about applicability of the model to the case of a typical passenger train.

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The authors declare that there are no conflicts of interest present.