RESEARCH OF APPROACHES TO CONSTRUCTING PREDICTIVE MODELS OF THE SPREAD OF VIRAL DISEASES
Last modified: 06.05.2021
Abstract
The article is devoted to the analysis of the available mathematical models in epidemiology and the possibility of their modification. We note that the situation with the COVID-19 virus pandemic is characterized by several features not comprehensively studied in the existing models. For a rational response to existing challenges, it is necessary to have a predictive and analytical apparatus in the complex (national and regional scale) mathematical models with a planning horizon of 2 years (the expected period of mass production of vaccines). The article discusses the existing approaches to predicting the spread of the COVID-19 virus in Russia based on mathematical models of epidemics. The possibilities and limitations of the proposed approaches are considered. In the conditions of the Russian Federation, transport connectivity at the interregional and intraregional levels plays an important role, and for megalopolises - transport flows within large agglomerations and the age structure of the population. In contrast to previous pandemics and epidemics, public policy plays a significant role. The approach, which consist in building multi-agent models that combine the advantages of compartment models and models based on the Monte Carlo method (individually oriented) is proposed by the authors. It is planned to use compartment models to assess the dynamics of the process and individually-oriented models - at the level of individual territories and districts.
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References
William Ogilvy Kermack and A. G. McKendrick, “A contribution to the mathematical theory of epidemics,” Proc. R. Soc. Lond. A, vol. 115, no. 772, pp. 700–721, 1927, doi: 10.1098/rspa.1927.0118.
H. W. Hethcote, “Three Basic Epidemiological Models,” in Biomathematics, Applied Mathematical Ecology, S. A. Levin, S. A. Levin, T. G. Hallam, and L. J. Gross, Eds., Berlin, Heidelberg: Springer Berlin Heidelberg, 1989, pp. 119–144.
H. W. Hethcote, “The Mathematics of Infectious Diseases,” SIAM Rev., vol. 42, no. 4, pp. 599–653, 2000, doi: 10.1137/S0036144500371907.
C. Bulut and Y. Kato, “Epidemiology of COVID-19,” Turkish journal of medical sciences, vol. 50, SI-1, pp. 563–570, 2020, doi: 10.3906/sag-2004-172.
H. W. Hethcote, J. W. van Ark, and J. M. Karon, “A simulation model of AIDS in San Francisco: II. Simulations, therapy, and sensitivity analysis,” Mathematical biosciences, vol. 106, no. 2, pp. 223–247, 1991, doi: 10.1016/0025-5564(91)90078-w.
H. W. Hethcote, J. W. van Ark, and I. M. Longini, “A simulation model of AIDS in San Francisco: I. Model formulation and parameter estimation,” Mathematical biosciences, vol. 106, no. 2, pp. 203–222, 1991, doi: 10.1016/0025-5564(91)90077-v.
R. M. Anderson, The Population dynamics of infectious diseases: Theory and applications / edited by Roy M. Anderson. London: Chapman and Hall, 1982.
F. Brauer, C. Castillo-Chavez, and Z. Feng, Mathematical Models in Epidemiology. New York, NY: Springer New York, 2019.
H. Hethcote, M. Zhien, and L. Shengbing, “Effects of quarantine in six endemic models for infectious diseases,” Mathematical biosciences, vol. 180, pp. 141–160, 2002, doi: 10.1016/s0025-5564(02)00111-6.
A. Kumar, K. Goel, and Nilam, “A deterministic time-delayed SIR epidemic model: mathematical modeling and analysis,” Theory in biosciences = Theorie in den Biowissenschaften, vol. 139, no. 1, pp. 67–76, 2020, doi: 10.1007/s12064-019-00300-7.
H. Loeffler-Wirth, M. Schmidt, and H. Binder, “Covid-19 Transmission Trajectories-Monitoring the Pandemic in the Worldwide Context,” Viruses, vol. 12, no. 7, 2020, doi: 10.3390/v12070777.
M. Melis and R. Littera, “Undetected infectives in the Covid-19 pandemic,” International journal of infectious diseases : IJID : official publication of the International Society for Infectious Diseases, 2021, doi: 10.1016/j.ijid.2021.01.010.
D. Rafiq, A. Batool, and M. A. Bazaz, “Three months of COVID-19: A systematic review and meta-analysis,” Reviews in medical virology, vol. 30, no. 4, e2113, 2020, doi: 10.1002/rmv.2113.
F. Rojas, L. Maurin, R. Dünner, and K. Pichara, “Classifying CMB time-ordered data through deep neural networks,” Monthly Notices of the Royal Astronomical Society, vol. 494, no. 3, pp. 3741–3749, 2020, doi: 10.1093/mnras/staa1009.
Simon A. Levin, “Applied Mathematical Ecology by Simon A. Levin (auth.)”, 1986.
P. J. Turk et al., “Modeling COVID-19 Latent Prevalence to Assess a Public Health Intervention at a State and Regional Scale: Retrospective Cohort Study,” JMIR public health and surveillance, vol. 6, no. 2, e19353, 2020, doi: 10.2196/19353.
H. M. Yang, L. P. Lombardi Junior, F. F. M. Castro, and A. C. Yang, “Mathematical model describing CoViD-19 in São Paulo, Brazil - evaluating isolation as control mechanism and forecasting epidemiological scenarios of release,” Epidemiology and infection, vol. 148, e155, 2020, doi: 10.1017/S0950268820001600.
C. Wolfram, “An Agent-Based Model of COVID-19,” ComplexSystems, vol. 29, no. 1, pp. 87–105, 2020, doi: 10.25088/ComplexSystems.29.1.87.
R. Yaari, A. Huppert, and I. Dattner, “A statistical methodology for data-driven partitioning of infectious disease incidence into age-groups,” Jul. 2019. [Online]. Available: https://arxiv.org/pdf/1907.03441
