title: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð¸Ð½ÑÐµÐºÑÐ¸Ð¹ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÐºÐ¾Ð¼Ð¿Ð°ÑÑÐ¼ÐµÐ½ÑÐ°Ð»ÑÐ½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Mathematical modeling of the spread of infections based on the compartmental model
Creators: name: ÐÐ»ÐµÐºÑÐµÐµÐ², ÐÐ»ÐµÐºÑÐµÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2025
Subjects: ÐºÐ¾Ð¼Ð¿Ð°ÑÑÐ¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸
Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÑÐ¿Ð¸Ð´ÐµÐ¼Ð¸Ð¾Ð»Ð¾Ð³Ð¸Ñ
sir
seir
seird
seairsd
Ð¸Ð½ÑÐµÐºÑÐ¸Ð¾Ð½Ð½ÑÐµ Ð·Ð°Ð±Ð¾Ð»ÐµÐ²Ð°Ð½Ð¸Ñ
covid-19
Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ¿Ð¸Ð´ÐµÐ¼Ð¸Ð¹
compartmental models
mathematical modeling
epidemiology
infectious diseases
epidemic forecasting

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð¸Ð½ÑÐµÐºÑÐ¸Ð¹ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÐºÐ¾Ð¼Ð¿Ð°ÑÑÐ¼ÐµÐ½ÑÐ°Ð»ÑÐ½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸Â». ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸Ð·ÑÑÐµÐ½Ð¸Ñ Ð¸ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÐºÐ¾Ð¼Ð¿Ð°ÑÑÐ¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð´Ð»Ñ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¸ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð¸Ð½ÑÐµÐºÑÐ¸Ð¾Ð½Ð½ÑÑ Ð·Ð°Ð±Ð¾Ð»ÐµÐ²Ð°Ð½Ð¸Ð¹. ÐÑÐ½Ð¾Ð²Ð½Ð¾Ðµ Ð²Ð½Ð¸Ð¼Ð°Ð½Ð¸Ðµ ÑÐ´ÐµÐ»ÐµÐ½Ð¾ Ð¼Ð¾Ð´ÐµÐ»ÑÐ¼ SEIR, SIRS, SEIRD Ð¸ SEAIRSD, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑÑÑ Ð´Ð»Ñ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ¿Ð¸Ð´ÐµÐ¼Ð¸Ð¹, Ð¾ÑÐµÐ½ÐºÐ¸ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð¸ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÐ¸ Ð¿ÑÐ¾ÑÐ¸Ð²Ð¾ÑÐ¿Ð¸Ð´ÐµÐ¼Ð¸ÑÐµÑÐºÐ¸Ñ Ð¼ÐµÑ. Ð Ð°Ð±Ð¾ÑÐ° Ð½Ð°Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð° Ð½Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÑ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¸ Ð¸Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð´Ð»Ñ Ð²ÑÑÐ²Ð»ÐµÐ½Ð¸Ñ Ð½Ð°Ð¸Ð±Ð¾Ð»ÐµÐµ ÑÐ¾ÑÐ½Ð¾Ð¹ Ð¸ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð² ÐºÐ¾Ð½ÑÐµÐºÑÑÐµ ÑÐµÐ°Ð»ÑÐ½ÑÑ Ð´Ð°Ð½Ð½ÑÑ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1) Ð¸Ð·ÑÑÐµÐ½Ð¸Ðµ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹ ÐºÐ¾Ð¼Ð¿Ð°ÑÑÐ¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹, Ð¸Ñ ÑÑÑÑÐºÑÑÑÑ Ð¸ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÐµÐ¹. 2) ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð¸ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð°Ñ Ð°Ð´Ð°Ð¿ÑÐ°ÑÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ SEIR, SIRS, SEIRD Ð¸ SEAIRSD. 3) Ð¾ÑÐµÐ½ÐºÐ° Ð¸ Ð¿Ð¾Ð´Ð±Ð¾Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð´Ð»Ñ ÐºÐ°Ð¶Ð´Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¼ÐµÑÐ¾Ð´Ð° Ð½Ð°Ð¸Ð¼ÐµÐ½ÑÑÐ¸Ñ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ¾Ð². 4) Ð°Ð½Ð°Ð»Ð¸Ð· ÑÑÐ²ÑÑÐ²Ð¸ÑÐµÐ»ÑÐ½Ð¾ÑÑÐ¸ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð¸ Ð¸Ñ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð½Ð° ÑÐ¾ÑÐ½Ð¾ÑÑÑ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¾Ð². 5) Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐ° ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð´Ð°Ð½Ð½ÑÑ Ð¿Ð¾ Ð¿Ð°Ð½Ð´ÐµÐ¼Ð¸Ð¸ COVID-19 Ð´Ð»Ñ ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹. 6) ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ñ ÑÐµÐ°Ð»ÑÐ½ÑÐ¼Ð¸ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸ Ð¸ Ð²ÑÐ±Ð¾Ñ Ð½Ð°Ð¸Ð±Ð¾Ð»ÐµÐµ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð´Ð»Ñ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ. 7) Ð¾ÑÐµÐ½ÐºÐ° ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¼ÐµÑÑÐ¸Ðº, ÑÐ°ÐºÐ¸Ñ ÐºÐ°Ðº RMSE Ð¸ MAE, Ð´Ð»Ñ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ð¸Ñ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÐ¸. Ð­ÑÐ¸ Ð·Ð°Ð´Ð°ÑÐ¸ Ð½Ð°Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ñ Ð½Ð° ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ðµ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ° Ð´Ð»Ñ ÑÐ¾ÑÐ½Ð¾Ð³Ð¾ Ð¸ Ð³Ð¸Ð±ÐºÐ¾Ð³Ð¾ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ¿Ð¸Ð´ÐµÐ¼Ð¸Ð¹, ÑÑÐ¾ Ð°ÐºÑÑÐ°Ð»ÑÐ½Ð¾ Ð´Ð»Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¼ÐµÑ Ð·Ð´ÑÐ°Ð²Ð¾Ð¾ÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð¸ Ð¿ÑÐµÐ´Ð¾ÑÐ²ÑÐ°ÑÐµÐ½Ð¸Ñ Ð¼Ð°ÑÑÑÐ°Ð±Ð½ÑÑ Ð¿Ð¾ÑÐ»ÐµÐ´ÑÑÐ²Ð¸Ð¹ Ð¸Ð½ÑÐµÐºÑÐ¸Ð¾Ð½Ð½ÑÑ Ð·Ð°Ð±Ð¾Ð»ÐµÐ²Ð°Ð½Ð¸Ð¹.
description: The subject of the graduate qualification work is Â« Mathematical modeling of the spread of infections based on the compartmental modelÂ». The work is devoted to the study and implementation of various compartmental models for analyzing the dynamics of the spread of infectious diseases. The focus is on SEIR, SIRS, SEIRD and SEAIRSD models, which are used for predicting epidemics, estimating the parameters and effectiveness of anti-epidemic measures. The work aims to develop mathematical methods and their application to identify the most accurate and efficient model in the context of real data. The objectives addressed in the study are: 1) study of the features of compartmental models, their structure and capabilities. 2) implementation and program adaptation of SEIR, SIRS, SEIRD and SEAIRSD models. 3) estimation and selection of parameters for each model using least squares method. 4) sensitivity analysis of model parameters and their impact on forecast accuracy. 5) processing statistical data on COVID-19 pandemic to test the models. 6) comparison of the results obtained with real data and selection of the most effective model for forecasting. 7) evaluating the accuracy of models based on metrics such as RMSE and MAE to quantitatively analyze their performance. These tasks are aimed at creating a tool for accurate and flexible epidemic forecasting, which is relevant for optimizing public health measures and preventing large-scale consequences of infectious diseases.