vmaitComputational Mathematics and Information TechnologiesComputational Mathematics and Information Technologies2587-8999Донской государственный технический университет10.23947/2587-8999-2020-1-1-19-30vmait-4Research ArticleСтатьиИсследование процессов распространения вирусных заболеваний на базе модификаций SIR-моделиStudy of the spread of viral diseases based on modifications of the SIR modelНикитинаА. В.NikitinaA. V.

Никитина Алла Валерьевна, Доктор технических наук, профессор, профессор кафедры Интеллектуальных и многопроцессорных систем

г. Таганрог, ул. Чехова, 2

8(951)516 85 38

Alla V. Nikitina, Dr.Sci., professor, Professor of the Department of Intelligent and multiprocessor systems

Chekhov st., 2, Taganrog

8(951)516 85 38

nikitina.vm@gmail.comЛяпуноваИ. А.LyapunovI. A.

Ляпунова Ирина Артуровна, Кандидат технических наук, доцент кафедры высшейматематики

г. Ростов-на-Дону, ул. Большая Садовая, 105/42

Irina A. Lyapunova, Ph.Dr., associate professor of the Higher Mathematics Department

105/42 Bolshaya Sadovaya Str., Rostov-on-Don, 344006

ialyapunova@sfedu.ruДудниковЕ. А.DudnikovE. A.

Дудников Евгений Александрович, Магистрант

г. Ростов-на-Дону, ул. Большая Садовая, 105/42

Evgeniy A. Ddudnikov, undergraduate student

105/42 Bolshaya Sadovaya Str., Rostov-on-Don, 344006

avnikitina@sfedu.ruЮжный федеральный университетРоссияSouthern Federal UniversityRussian Federation202020022023411930Copyright © Никитина А.В., Ляпунова И.А., Дудников Е.А., 20232023Никитина А.В., Ляпунова И.А., Дудников Е.А.Nikitina A.V., Lyapunov I.A., Dudnikov E.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.cmit-journal.ru/jour/article/view/4

Распространение инфекционных заболеваний представляет собой сложное явление с множеством взаимодействующих факторов. Ключевая роль математической эпидемиологии заключается в создании моделей распространения патогенов. Эти модели служат в качестве математической основы для понимания сложной динамики распространения заболевания. Существуют различные математические модели эпидемий, но в зависимости от типа эпидемии возникает необходимость их тщательного анализа и совершенствования. В 1927 году Кермак У. и Маккендрик А. опубликовали свою теорию, на базе которой была построена SIR-модель (Susceptible-Infected-Removed). Данная теория представляла собой гипотезу о распространении инфекционного заболевания среди населения. Эта модель до сих пор не потеряла актуальности и хорошо подходит для прогнозирования процесса распространения инфекционных заболеваний.Цель работы состояла в разработке и исследовании математической модели распространения эпидемии на основе существующих моделей эпиддинамики. В работе исследованы процессы протекания эпидемий с помощью классической SIR-модели и её модификаций: SEIRD-модели (Susceptible-Еxposed-Infected-Removed-Dead) и SEIHFR-модели (Susceptible-Еxposed-Infected-Hospitalized-Funeral-Removed). Проведено численное моделирование динамики распространения вирусной болезни при различных сценариях ее протекания. Исследованы современные методы и средства математического моделирования процессов распространения вирусных заболеваний; проанализирована их эффективность в зависимости от типа эпидемии. Предложены новые модификации известных моделей на основе систем дифференциальных уравнений, учитывающие особенности приобретения иммунитета, а также эффект запаздывания при обнаружении зараженных людей. Исследована чувствительность параметров, входящих в модели.Полученные результаты могут быть использованы для исследования процессов протекания современных эпидемий, в том числе коронавирусной пандемии, а также для эффективного прогнозирования динамики заболеваемости, разработки эффективных механизмов сдерживания и контроля эпидемий локального и глобального характеров.

The spread of infectious diseases is a complex phenomenon with many interacting factors. The key role of mathematical epidemiology is to create pathogen spread patterns. These models serve as the mathematical basis for understanding the complex dynamics of the spread of the disease. There are various mathematical models of epidemics, but depending on the type of epidemic, there is a need for their careful analysis and improvement. In 1927, Kermak W. and Mackendrick A. published their theory, on the basis of which the SIR-model (Susceptible-Infected-Removed) was built. This theory was a hypothesis about the spread of an infectious disease among the population. This model has still not lost its relevance and is well suited for predicting the spread of infectious diseases. The aim of the work was to develop and study a mathematical model of the spread of the epidemic based on existing models of epidynamics.The work investigated the processes of epidemics using the classical SIR model and its modifications: SEIRD models (Susceptible-Exposed-Infected-Removed-Dead) and SEIHFRmodels (Susceptible-Exposed-Infected-Hospitalized-Funeral-Removed). A numerical simulation of the dynamics of the spread of viral disease in various scenarios of its course has been carried out. The modern methods and means of mathematical modeling of the spread of viral diseases have been investigated; analyzed their effectiveness depending on the type of epidemic. New modifications of well-known models based on systems of differential equations that take into account the characteristics of the acquisition of immunity, as well as the effect of delay in detecting infected people, are pro-posed. The sensitivity of the parameters included in the model is investigated.The results can be used to study the processes of modern epidemics, including the coronavirus pandemic, as well as to effectively predict the dynamics of the disease, to develop effective mechanisms to contain and control epidemics of a local and global nature.

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