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Valery Akimov, Ekaterina Ivanova, Irina Oltyan
STATISTICAL MODELS FOR FORECASTING RT&A, No 4 (76) EMERGENCY SITUATIONS_Volume 18, December 2023
STATISTICAL MODELS FOR FORECASTING EMERGENCY SITUATIONS OF A BIOLOGICAL AND
SOCIAL CHARACTER
Valery Akimov, Ekaterina Ivanova, Irina Oltyan
Federal State Budgetary Institution "All-Russian Research Institute for Civil Defense and Emergencies of the Ministry of Emergency Situations of Russia" (Federal Center for Science and
High Technologies) akimov@vniigochs. ru
Abstract
The article considers a statistical model for predicting emergency situations of a biological and social nature. Particular attention is paid to the calculation of indicators of resource provision of the medical care system and mortality rates during the spread of the epidemic.
Keywords: forecasting model; Bayesian classifiers; emergency situations of a biological and social nature; indicators of resource provision of the medical care system; mortality rates during the spread of the epidemic.
I. Introduction
The spread of the new coronavirus infection COVID-19 in the world in three years has led to more than five hundred million infections and more than six million deaths. The high dynamics of growth in morbidity and mortality has led not only to a serious burden on the healthcare system in almost all countries of the world, but also to the development of scientific methods for modeling epidemics and pandemics. In particular, in [1], a statistical model for predicting epidemics using Bayesian classifiers is proposed.
The main input data for the formation of the basic training set of this model are the following groups of parameters: input data characterizing the settlement (hereinafter - NP); input data characterizing the socio-economic indicators of the NP; input data characterizing the composition and size of the population of the NP; input data characterizing the demographic indicators of the NP; input data characterizing the symptoms and course of a respiratory viral disease (hereinafter referred to as RVD); input data characterizing the level of provision of the population with medical care resources in the settlement; input data characterizing the epidemiological situation in the NP (with the development of an epidemic caused by RVD); results of forecasting and modeling of the spread of the epidemic caused by the PR in the NP.
II. Methods
Calculation of indicators of resource provision of the medical care system.
Valery Akimov, Ekaterina Ivanova, Irina Oltyan
STATISTICAL MODELS FOR FORECASTING RT&A, No 4 (76) EMERGENCY SITUATIONS_Volume 18, December 2023
The indicators of the availability of resources for the system of providing medical care in the territory during the spread of the epidemic include [2]: the indicator of the availability of hospitalized infectious patients with beds; indicator of availability of oxygen concentrators; indicator of availability of intensive care beds; the indicator of availability of artificial lung ventilation devices (hereinafter - ALV); indicator of provision of medical institutions with senior medical personnel; indicator of provision of medical institutions with paramedical personnel. The indicator of bed capacity of hospitalized infectious patients (lib) is determined by the formula [3]:
. _ KkH Kgi
Where:
KK ii - the number of beds for hospitalized infectious patients, units; Kgi - the total number of hospitalized infectious patients, people. The index of provision with oxygen concentrators ((Ikk) is determined by the formula:
IS
J _ ^K.KK
' KK _ "¡7 •
KKK
Where:
KK.KK — number of oxygen concentrators, units;
KKK — the total number of hospitalized, with the need for oxygen supply, pers. The indicator of provision with an intensive care bed fund (lit) is determined by the formula:
j _ KK.it 'it
Ktb
Where:
KKit — number of beds in the intensive care unit (hereinafter referred to as RIIT), units.; Ktb — total number of hospitalized infectious patients, pers. The indicator of provision with ventilators (or similar devices) (Im) is determined by the formula:
. _ ^a.ivl
Hvl ,
^ivl
Where:
Ka.ivi — number of ventilators (or similar devices), units;
Kivi — total number of hospitalized infectious patients with the need to connect to ventilators (or similar devices), people
The indicator of provision of medical institutions with senior medical personnel (Istmp) is determined by the formula:
. _ ^stmp
* s tmp j}
Where:
Kstmp — indicator of senior medical personnel, people; Kgi — total number of hospitalized infectious patients, pers.
The indicator of provision of medical institutions with paramedical personnel (Isrmp, units per 1000 people) is determined by the formula:
IS
. _ ^srmp
* srmp 7}
Kgi
Where:
Ksrmp — indicator of the average medical personnel, people; Kgi — total number of hospitalized infectious patients, pers.
Calculation of mortality rates during the spread of the epidemic
Valery Akimov, Ekaterina Ivanova, Irina Oltyan STATISTICAL MODELS FOR FORECASTING EMERGENCY SITUATIONS
RT&A, No 4 (76) Volume 18, December 2023
The indicators of mortality during the spread of the epidemic and in the conditions of its absence include [2]: the mortality rate due to respiratory diseases during the spread of the epidemic; mortality rate due to diseases of the circulatory system during the spread of the epidemic; mortality rate due to neoplasms during the spread of the epidemic; overall mortality rate due to respiratory diseases, diseases of the circulatory system and neoplasms during the spread of the epidemic (in the absence of it).
The mortality rate due to respiratory diseases ((Isod, units per 1000 people) is determined by the formula [4]:
Isod =-^•1000,
Where:
KSOd — the number of deaths due to respiratory diseases per month, people;
Knp — population of the settlement, pers.
Mortality rate due to diseases of the circulatory system (L», unit per 1000 people.) is determined by the formula:
^=^•1000,
TS
^np
Where:
KSbk — the number of deaths due to diseases of the circulatory system per month, people;
Knp — population of the settlement, pers. The mortality rate due to neoplasms (Isn) is determined by the formula:
Isn=jr^i000,
^np
Where:
Ksn — the number of deaths due to neoplasms per month, people;
Ksp — population of the settlement, pers.
Then the overall mortality rate due to respiratory diseases, diseases of the circulatory system and neoplasms during the spread of the epidemic is determined by the following relationship:
Ism Isod + Isbk + Isn,
Where:
ISod — mortality rate due to respiratory diseases, units. per 1000 people;
ISbk — mortality rate due to diseases of the circulatory system, units. per 1000 people;
Isn — mortality rate due to neoplasms, units per 1000 people.
III. Results
Thus, this article considers a statistical model for predicting emergency situations of a biological and social nature. Particular attention is paid to the calculation of indicators of resource provision of the medical care system and mortality rates during the spread of the epidemic.
IV. Discussion
The discussion of the verbal and mathematical foundations of predictive modeling of emergency situations of a biological and social nature during the development of an epidemic caused by EIA is quite active in the scientific literature [5-10].
Valery Akimov, Ekaterina Ivanova, Irina Oltyan
STATISTICAL MODELS FOR FORECASTING RT&A, No 4 (76) EMERGENCY SITUATIONS_Volume 18, December 2023
At the previous conference RISK - 2022, the authors presented reports on the issues of predictive modeling of natural and man-made emergencies [11, 12].
References
[1] Predictive and analytical solutions for natural, man-made and biological and social threats of a unified system of information and analytical support for the safety of the environment and public order "Safe City" / V. A. Akimov, A. V. Mishurny, O. V. Yakimyuk [and etc.]. - Moscow: All-Russian Research Institute for Civil Defense and Emergency Situations of the Ministry of Emergency Situations of Russia, 2022. - 315 p. - ISBN 978-593970-278-2. - EDN MGXNYI.
[2] Akimov, V. A. Determining the indicators of resource provision of the medical care system and mortality rates during the spread of the epidemic / V. A. Akimov, O. A. Derendyaeva, E. O. Ivanova // Application of mathematical methods to problem solving EMERCOM of Russia: Proceedings of Section No. 14 of the XXIII International Scientific and Practical Conference, Khimki, March 01, 2023. - Khimki: Academy of Civil Protection of the Ministry of the Russian Federation for Civil Defense, Emergency Situations and Elimination of Consequences of Natural Disasters named after Lieutenant General D.I. Mikhailika, 2023. - S. 18-22. - EDNETMRTH.
[3] Akimov, V. A. Mathematical models for predicting the consequences of mass diseases of people / V. A. Akimov, E. O. Ivanova, O. A. Derendyaeva // Civil defense on guard of peace and security: Proceedings of the VII International Scientific and Practical conference dedicated to World Civil Defense Day. In the year of the 90th anniversary of the formation of the Academy of the State Fire Service of the Ministry of Emergency Situations of Russia: in 5 parts, Moscow, March 01, 2023. Volume Part V. - Moscow: Academy of the State Fire Service of the Ministry of the Russian Federation for Civil Defense, Emergencies and Disaster Relief, 2023. - P. 227-233. - EDN TLQAQX.
[4] Akimov, V. A. Mathematical models of epidemics and pandemics as sources of emergency situations of a biological and social nature / V. A. Akimov, M. V. Bedilo, E. O. Ivanova // Civil Security Technologies. - 2022. - T. 19, No. 3 (73). - P. 10-14. - EDN IPFEND.
[5] Akimov, V. A. Modern methods of studying emergency situations of natural, technogenic and biological and social nature / V. A. Akimov, M. V. Bedilo // Civil defense on guard of peace and security: Materials of the VI International scientific and practical conference dedicated to World Civil Defense Day. In 4 parts, Moscow, March 01, 2022 / Comp. V.S. Butko, M.V. Aleshkov, S.V. Podkosov, A.G. Zavorotny [i dr.]. Volume Part I. -Moscow: Academy of the State Fire Service of the Ministry of the Russian Federation for Civil Defense, Emergencies and Disaster Relief, 2022. - P. 16-24. - EDN HSSYVB.
[6] Akimov, V. A., Bedilo M. V., Sushchev S. P. Study of emergency situations of natural, technogenic and biological and social nature by modern scientific methods. -Moscow: All-Russian Research Institute for Civil Defense and Emergencies of the Ministry of Emergency Situations of Russia, 2021. - 179 p. - ISBN 978-5-93970-249-2. - EDN WUKXKC.
[7] Security of Russia. Legal, socio-economic and scientific and technical aspects. Analysis and provision of security from emergency situations / V. A. Akimov, A. A. Antyukhov, E. V. Arefieva [and others]; Security Council of the Russian Federation, Russian Academy of Sciences, EMERCOM of Russia, Rostekhnadzor, Russian Science Foundation, Rostec State Corporation, Rosatom State Corporation, Rosneft Oil Company PJSC, Russian Railways OJSC, Transneft PJSC, Gazprom PJSC. - Moscow: MGOF "Knowledge", 2021. - 500 p. - ISBN 978-5-87633-199-1. - EDN FXIJPZ.
Valery Akimov, Ekaterina Ivanova, Irina Oltyan
STATISTICAL MODELS FOR FORECASTING RT&A, No 4 (76) EMERGENCY SITUATIONS_Volume 18, December 2023
[8] Akimov, V. A. Technique of ranking emergency situations of natural, technogenic and biological-social nature according to the degree of their catastrophicity / V. A. Akimov, I. Yu. Oltyan, E. O. Ivanova // Civil Security Technologies. - 2021. - T. 18, No. 1 (67). - P. 4-7. - DOI 10.54234/CST.19968493.2021.18.1.67.1.4. - EDN IOGGXC.
[9] Akimov, V. A. Applications of the General Theory of Safety to the Study of Emergency Situations of a Natural, Technogenic and Biological and Social Character / V. A. Akimov // Civil Security Technologies. - 2021. - T. 18, No. S. - P. 13-28. - DOI 10.54234/CST.19968493.2021.18.S.2.13. - EDN LRYKFU.
[10] Akimov, V. A. Investigation of emergency situations of natural, technogenic and biological and social nature by methods of post-non-classical science: problem statement / V. A. Akimov, A. I. Ovsyanik, E. O. Ivanova // Fires and emergency situations : prevention, elimination. - 2021. - No. 2. - P. 95-100. - DOI 10.25257/FE.2021.2.95-100. - EDN YBDTJO.
[11] Akimov, V. Forecast of natural emergency situations with modern methods / V. Akimov, M. Bedilo, O. Derendiaeva, E. Ivanova, I. Oltyan // RT&A, Special Issue No. 4 (70), Volume 17, November 2022. - S. 71 - 77. - DOI: https://doi.org/10.24412/1932-2321-2022-470-71-77.
[12] Akimov, V. Forecast modeling of man-made emergencies with modern methods/ V. Akimov, M. Bedilo, O. Derendiaeva, E. Ivanova, I. Oltyan // RT&A, Special Issue No. 4 (70), Volume 17, November 2022. - S. 318 - 323. - DOI: https://doi .org/10.24412/1932-2321-2022-470-318-323
