title: ÐÐ±ÑÐ°ÑÐ½ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð´Ð»Ñ ÑÐ¿Ð¸Ð´ÐµÐ¼Ð¸Ð¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð² ÑÑÐµÐ´Ðµ AnyDynamics
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Inverse problems for epidemiological models in the AnyDynamics environment
Creators: name: ÐÐµÐ»ÑÐ²Ð¸Ð½Ð°, Ð®Ð»Ð¸Ñ
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: 2023
Subjects: AnyDynamics
Ð¾Ð±ÑÐ°ÑÐ½ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸
ÑÐ¿Ð¸Ð´ÐµÐ¼Ð¸Ð¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸
inverse problems
epidemiological models

description: Ð­ÑÐ° ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¼Ð¾Ð´ÐµÐ»ÑÐ¼ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ Ð¸Ð½ÑÐµÐºÑÐ¸Ð¹, Ð½Ð°Ð¿ÑÐ¸Ð¼ÐµÑ, covid-2019 Ð¸Ð»Ð¸ Ð´ÑÑÐ³Ð¸Ñ Ð²Ð¸ÑÑÑÐ¾Ð², Ð² Ñ.Ñ. Ð²ÑÐµÐ´Ð¾Ð½Ð¾ÑÐ½Ð¾Ð³Ð¾ ÐÐ Ð¸Ð»Ð¸ Ð½ÐµÐ¶ÐµÐ»Ð°ÑÐµÐ»ÑÐ½Ð¾Ð¹ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸. Ð¦ÐµÐ»Ñ ÑÑÐ¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ Ð·Ð°ÐºÐ»ÑÑÐ°ÐµÑÑÑ Ð² ÑÐ¾Ð¼, ÑÑÐ¾Ð±Ñ ÑÐµÑÐ¸ÑÑ Ð¾Ð±ÑÐ°ÑÐ½ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð´Ð»Ñ ÑÐ°Ð·Ð½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð½Ð° ÑÐ°Ð·Ð½ÑÑ Ð¿ÑÐ¾Ð¼ÐµÐ¶ÑÑÐºÐ°Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð¸, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑ ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð´Ð°Ð½Ð½ÑÐµ Ð´Ð»Ñ covid-19, Ð¸ Ð²ÑÑÑÐ½Ð¸ÑÑ, Ð¼Ð¾Ð¶Ð½Ð¾ Ð»Ð¸ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÑ AnyDynamics Ð´Ð»Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð¾Ð±ÑÐ°ÑÐ½ÑÑ Ð·Ð°Ð´Ð°Ñ. ÐÐ»Ñ ÑÑÐ¾Ð³Ð¾ Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ñ ÑÐ»ÐµÐ´ÑÑÑÐ¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸: 1. ÐÐ¿ÑÐµÐ´ÐµÐ»Ð¸ÑÑ ÑÐµÐ»ÐµÐ²Ð¾Ð¹ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð» Ð´Ð»Ñ ÐºÐ°Ð¶Ð´Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸. 2. ÐÐ¾Ð´Ð³Ð¾ÑÐ¾Ð²Ð¸ÑÑ Ð¸ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐ°ÑÑ ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð´Ð°Ð½Ð½ÑÐµ Ð´Ð»Ñ covid-2019. 3. ÐÐ°Ð¹ÑÐ¸ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð²ÑÑÑÐ¾ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¾ÑÐ°. 4. Ð¡ÑÐ°Ð²Ð½Ð¸ÑÑ Ð³ÑÐ°ÑÐ¸ÐºÐ¸, Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð½ÑÐ¼Ð¸ Ð¿Ð¾ ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ð¼ Ð´Ð°Ð½Ð½ÑÐ¼, Ð¸ Ð³ÑÐ°ÑÐ¸ÐºÐ¸ Ð¿ÐµÑÐµÐ¼ÐµÐ½Ð½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹, ÑÑÐ°ÑÑÐ²ÑÑÑÐ¸Ñ Ð² ÑÐµÐ»ÐµÐ²Ð¾Ð¼ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»Ðµ. ÐÑÐµ Ð¾Ð±ÑÐ°ÑÐ½ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÑÐµÐ´Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ AnyDynamics Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð²ÑÑÑÐ¾ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð² ÑÑÑ ÑÑÐµÐ´Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¾ÑÐ°. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð¼ ÑÑÐ¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ° Ð¼Ð¾Ð´ÑÐ»ÐµÐ¹ ÑÐµÑÐµÐ½Ð¸Ñ Ð¾Ð±ÑÐ°ÑÐ½ÑÑ Ð·Ð°Ð´Ð°Ñ, ÐºÐ°Ð¶Ð´ÑÐ¹ Ð¸Ð· ÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ¾Ð´ÐµÑÐ¶Ð¸Ñ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ðµ ÑÐµÐ»ÐµÐ²Ð¾Ð³Ð¾ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»Ð°, Ð¿Ð¾ÑÑÑÐ¾Ð¸ÑÐµÐ»Ñ Ð³ÑÐ°ÑÐ¸ÐºÐ¾Ð² Ð¿Ð¾ ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ð¼ Ð´Ð°Ð½Ð½ÑÐ¼ Ð¸ ÑÐ¸ÑÑÐµÐ¼Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹, Ð´Ð»Ñ ÐºÐ¾ÑÐ¾ÑÐ¾Ð¹ ÑÐµÑÐ°ÐµÑÑÑ Ð¾Ð±ÑÐ°ÑÐ½Ð°Ñ Ð·Ð°Ð´Ð°ÑÐ° Ð¸ ÑÑÑÐ¾ÑÑÑÑ Ð³ÑÐ°ÑÐ¸ÐºÐ¸ Ð´Ð»Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ Ð³ÑÐ°ÑÐ¸ÐºÐ°Ð¼Ð¸ Ð¿Ð¾ ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ð¼ Ð´Ð°Ð½Ð½ÑÐ¼. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÑÐ¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ Ð¼Ð¾Ð¶Ð½Ð¾ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸ÑÑ Ð² ÑÐ°Ð·Ð½ÑÑ Ð¾Ð±Ð»Ð°ÑÑÑÑ ÑÐ°ÐºÐ¸Ñ, ÐºÐ°Ðº Ð¼ÐµÐ´Ð¸ÑÐ¸Ð½Ð°, ÐºÐ¸Ð±ÐµÑÐ±ÐµÐ·Ð¾Ð¿Ð°ÑÐ½Ð¾ÑÑÑ, ÑÐ¾ÑÐ¸Ð¾Ð»Ð¾Ð³Ð¸Ñ Ð¸ Ñ.Ð´., Ð´Ð»Ñ Ð¸Ð·ÑÑÐµÐ½Ð¸Ñ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ ÑÐ¿Ð¸Ð´ÐµÐ¼Ð¸Ð¹, Ð° ÑÐ°ÐºÐ¶Ðµ Ð²ÑÐ±Ð¾ÑÐ° Ð¼ÐµÑ Ð¿ÑÐ¾ÑÐ¸Ð²Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ ÑÐ¿Ð¸Ð´ÐµÐ¼Ð¸Ð¸.
description: This work is devoted to models of the spread of infections, for example, covid-2019 or other viruses, incl. malware or unwanted information. The purpose of this work is to solve inverse problems for different models at different time intervals using statistics for covid-19 and to find out if AnyDynamics can be used to solve inverse problems. For this, the following tasks are set: 1. Determine the target functional for each model. 2. Prepare and process statistical data for covid-2019. 3. Find parameters using the built-in optimizer. 4. Compare graphs built on the basis of statistical data and graphs of model variables involved in the target functional. All inverse problems were solved in the AnyDynamics modeling environment using the optimizer built into this environment. The result of this work is a library of modules for solving inverse problems, each of which contains the calculation of the objective functional, a graph builder for statistical data and a model equation system for which the inverse problem is solved and graphs are built for comparison with graphs for statistical data. The results of this work can be applied in various fields such as medicine, cybersecurity, sociology, etc., to study the spread of epidemics, as well as the choice of measures to counter the epidemic.