National characteristics of changes in the hazard of development of the COVID-19 coronavirus pandemic: mathematical modeling and statistical analysis
Research Article
Acknowledgments
The research was carried out under the State assignment AAAA-A17-117041910167-0
How to Cite
Cherkashin A.K. National characteristics of changes in the hazard of development of the COVID-19 coronavirus pandemic: mathematical modeling and statistical analysis. Population. 2020. Vol. 23. No. 3. P. 83-95. DOI: https://doi.org/10.19181/population.2020.23.3.8 (in Russ.).
Abstract
The article develops models and methods for calculating quantitative indicators of the response of the national state and society to the hazard of spreading COVID-19 coronavirus infection in different countries. There are used the concepts, models and methods in reliability theory to describe the development of the epidemiological situation with probability functions (possibilities) of no-failure operations (survival, health protection), probability density (distribution) of the failure (infection rates), integrated hazard of infection, failure rate (risk to take ill), acceptable risk, and manageability of the epidemic situation. Government control is carried out through pressure on the acceptable risk. Based on the results of statistical processing of data on the number of confirmed cases of the disease in different countries, a comparative analysis of the epidemic process in different national circumstances of the fight against the world pandemic was conducted. The reliability functions are based on a double interpretation of the equation of changes in the hazard measure over time and on the factors of development of the epidemic process, in particular, the age structure of the population is taken into account. The mathematical and statistical analyses are based on the exponential hazard equation, which is represented in a semi-logarithmic scale by a linear dependence on time. Nonlinear distortions are due to variations in the controlled value of acceptable risk and show national features of regulating the epidemic load on the population. The results obtained confirm the model's efficiency in clear terms of reliability theory and determine the direction of its improvement in the context of an ongoing global pandemic on the basis of newly emerging data and circumstances for a better understanding of the features of current processes across countries and continents.
Keywords:
COVID-19 pandemic, country features of epidemic curves, mathematical models of infection hazard, preparedness indicator, situational manageability
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2. Global Health Security Index. Available at: https://www.ghsindex.org/wp-content/uploads/2019/10/2019-Global-Health-Security-Index.pdf (Accessed: 16 March 2020).
3. Katkova I. P. Rossijskoe zdravoohranenie v kontekste zadach dostizheniya vseobshchej dostupnosti uslug zdravoohraneniya k 2030 godu [Russian healthcare in the context of achieving universal access to health services by 2030]. Narodonaselenie [Population]. 2020. Vol. 23. No. 1. P. 135-147. DOI: 10.19181/population.2020.23.1.11 (in Russ.)
4. Budilova E. V., Lagutin M. B., Migranova L. A. Vliyaniye demograficheskih i social'no-ekonomicheskih faktorov na popul'acionnoye zdorov'e naseleniya [Impact of the demographic and socio-economic factors on the population health]. Narodonaselenie [Population]. 2019. No. 3. P. 80¬92. DOI: 10.24411/1561-7785-2019-00028 (in Russ.)
5. Aaltola M. Covid-19 — a trigger for global transformation? Political distancing, global decoupling and growing distrust in health governance. FIIA Working Papers. 2020. No. 113. P. 4-14.
6. Denis M., Vandeweerd V., Verbeke R., Van der Vliet D. Overview of information available to support the development of medical countermeasures and interventions against COVID-19. Version dd. 30, 2020. Transdisciplinary Insights. P. 1-134.
7. Cohen J. Scientists are racing to model the next moves of a coronavirus that's still hard to predict. Science. 7 February 2020. Available at: https://www.sciencemag.org/news/2020/02/scientists-are-racing-model-next-moves-coronavirus-thats-still-hard-predict (Accessed: 18 April 2020).
8. Kermack W, McKendrick A. Contributions to the mathematical theory of epidemics, part III. Further studies of the problem of endemicity. Bulletin of Mathematical Biology. 1991. Vol.5. No. 3(1-2). P. 89-118.
9. Bailey N. Matematika v biologii i meditsine [Mathematics in Biology and Medicine]. Moscow. Mir [World]. 1970. 326 p. (in Russ.)
10. Zhang G., Pang H., Xue Y., Zhou Y., Wang R. Forecasting and analysis of time variation of parameters of COVID-19 infection in China using an improved SEIR model. Centre for Mathematical Modelling of Infectious Diseases COVID-19 working group. The Lancet. March 11, 2020. Available at: www.thelancet.com/inffection. (Accessed: 18 March 2020).
11. Vladimirov I. N., Myasnikova S. I., Cherkashin A. K. Geoinformatsionnoye obespecheniye otsenki zabolevaniya ptich'im grippom v regione [Geoinformation support for avian influenza disease assessment in the region]. Izvestiya RAN. Seriya geograficheskaya [RAS News. Geographical Series]. 2008. No. 2. P. 122-131. (in Russ.)
12. Huang C. Y., Wen T. H., Tsai Y. S. A Novel four-layer model for simulating epidemic dynamics and assessing intervention policies. Hindawi Publishing Corporation. Journal of Applied Mathematics. Vol. 2013. P. 1-20.
13. Cherkashin A. K. Polisistemnoye modelirovaniye [Polysystem Modeling]. Novosibirsk. Nauka [Science]. 2005. 280 p. (in Russ.)
14. Therneau T. M., Grambsch P. M. Modeling Survival Data: Extending the Cox Model. New York. Springer-Verlag. 2000. 355 p.
15. Cherkashin A. K. Otsenka kachestva zhizni na osnove resheniya obratnoj zadachi modelirovaniya dinamiki chislennosti naseleniya [Quality of life evaluation on the basis of inverse modeling of population dynamics]. Narodonaselenie [Population]. No. 1. 2014. P. 54-67. (in Russ.)
16. Cherkashin A. K., Krasnoshtanova N. E. Modelirovaniye otsenki riska hozajstvennoj deyatel'nosti v rajonah novogo neftegazovogo osvoeniya [Modeling of risk assessment of economic activity in areas of new oil and gas development]. Problemy analiza riska [Issues of Risk Analysis]. 2015. Vol. 12. No. 6. P. 44-52. (in Russ.)
17. Sklyanova I. P., Cherkashin A. K. Kolichestvennaya otsenka demograficheskoj reaktsii na izmeneniya uslovij zhiznedeyatel'nosti v monogorodah [Quantitative assessment of demographic response to changes in living conditions in single-industry towns]. Region: ekonomika i sotsiologiya [Region: Economics and Sociology]. 2015. No. 4. P. 179-197.
18. Roser M., Ritchie H., Ortiz-Ospina E. Coronavirus disease (COVID-19): Statistics and research. Our World in Data. 2020. Available at: https://ourworldindata.org/coronavirus/ (Accessed: 1 April 2020).
19. Gavrilov L. A., Gavrilova N. S. Reliability theory of aging and longevity. Handbook of the Biology of Aging. Sixth edition. Academic Press. San Diego, CA. USA. 2006. P. 3-42.
20. Cherkashin A. K., Leshchenko Ya. A., Boeva A. V. Dinamicheskie i kvalimetricheskiye modeli otsenki kachestva zhizni sem'i [Dynamic and qualimetric models of estimating quality of life of family]. Narodonaselenie [Population]. No. 3, 2015. P. 61-76. (in Russ.)
21. Hoyland A., Rausand M. System Reliability Theory: Models and Statistical Methods. New Jersey. John Wiley& Sons Inc. 2004. 518 p.
22. Severtsev N. A., Dedkov V. K. Metodologicheskiye voprosy nadozhnosti i bezopasnosti [Methodological issues of reliability and security]. Vestnik TvGU. Seriya: Prikladnaya matematika [Bulletin of Tver State University. Series: Applied Mathematics]. 2007. No. 3(6). P. 123-128. (in Russ.)
23. Kamke E. Spravochnik po differencial'nym uravneniyam v chastnyh proizvodnyh pervogo poryadka [Handbook on First-Order Partial Differential Equations]. Moscow. Nauka [Science]. 1966. 260 p. (in Russ.)
24. Naskol'ko opasen koronavirus: zaraznost', letal'nost' i gruppy riska [How dangerous is the coronavirus: infectivity, lethality, and risk groups]. Available at: https://ria.ru/20200319/1568742369.html?in=t (Accessed: 18 April 2020). (in Russ.)
Article
Received: 05.05.2020
Accepted: 25.09.2020
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Other cite formats:
APA
Cherkashin, A. K. (2020). National characteristics of changes in the hazard of development of the COVID-19 coronavirus pandemic: mathematical modeling and statistical analysis. Population, 23(3), 83-95. https://doi.org/10.19181/population.2020.23.3.8
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ISSUES OF HEALTHCARE AND SOCIAL SERVICES
