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9moment, we have provided testing calculations using simulated data. Now we are testing our approach on
real data.
References:
1. Y. Wang, D. Lukyanenko, A. Yagola. Magnetic parameters inversion method with full tensor gradient data //
Inverse Problem and Imaging. 2019. V. 13, no. 4. P. 745-754, DOI. 10.3934/ipi.2019034.
2. Y. Wang, I. Kolotov, D. Lukyanenko, A. Yagola. Reconstruction of Magnetic Susceptibility Using Full
Magnetic Gradient Data June 2020 Computational Mathematics and Mathematical Physics 60(6):1000-1007,
DOI: 10.1134/S096554252006010X.
A diffusion-convection problem with a fractional derivative along the trajectory of motion
A. V. Lapin1, V. V. Shaidurov2
1Sechenov University, Moscow
2Institute of Computational Modeling, Siberian branch of RAS, Krasnoyarsk
Email: avlapine@mail.ru
DOI 10.24412/cl-35065-2021-1-00-36
A new mathematical model of the diffusion-convective process with "memory along the flow path" is pro-
posed. This process is described by a homogeneous one-dimensional Dirichlet problem with a fractional deriv-
ative along the characteristic curve of the convection operator, or, in other words, with fractional material de-
rivative. A finite-difference scheme is constructed using an analogue of the well-known L1-approximation of
time-fractional derivative for the fractional material derivative and the conventional approximation of the dif-
fusion term.. The unique solvability of the constructed mesh scheme is proved. The stability estimates are de-
rived in the uniform mesh norm, and the accuracy estimates are given under the assumptions of sufficient
smoothness of the initial data and the solution of the differential problem. The presented results are based on
the article [1].
This work was supported by the Russian Scientific Foundation (grant 20-61-46017).
References
1. Lapin A. V., Shaidurov V.V. A diffusion-convection problem with a fractional derivative along the trajectory of
motion// RJNAMM. 2021. V.36, N.3. P. 157-163.
Numerically statistical investigation of efficacy of SEIR model
G. Z. Lotova1,2, V. L. Lukinov1,2, M. A. Marchenko1,2, G. A. Mikhailov1, D. D. Smirnov1
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: lot@osmf.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-82
A comparative analysis of the differential and the corresponding stochastic Poisson SEIR-models [1, 2] was
performed for the testing problem of the epidemic COVID-19 in Novosibirsk modeling in the period from the
23rd of March 2020 to the 21th of June 2020, with the initial population N = 2 798 170 [3]. By varying the ini-
tial population in the form N = n � m with m . 2, it was shown that the average values of the sick identified was
less (beginning with the 7th of April 2020) the corresponding differential values by the quantity that is statisti-
cally not distinguished from C(t)/m, with C . 27.3 on the 21th June. This relationship allows to use the stochas-
tic model for big population N. Practically useful confidential interval �three sigma� for the time interval from
the 1th of June 2020 to the 21th of June 2020 is about 110 % (as to the statistical average) and involves the
corresponding experimental estimates. The influence on the prognosis of introduction the delay, i. e. the incu-
bation period corresponding to Poisson model, was also investigated.
This work was carried out under state contract with ICMMG SB RAS (0251-2021-0002).
References
1. I. Sazonov, D. Grebennikov, M. Kelbert, G. Bocharov, Modelling Stochastic and Deterministic Behaviours in Virus
Infection Dynamics // Math. Model. Nat. Phenom., V. 12, No. 5, 2017, pp. 63-77.
2. N. V. Pertsev, K. K. Loginov, V. A. Topchii, �Analysis of a stage-dependent epidemic model based on a non-Markov
random process�, Sib. Zh. Ind. Mat., 23:3 (2020), 105�122; J. Appl. Industr. Math., 14:3 (2020), 566�580.
3. O. I. Krivorotko, S. I. Kabanikhin, N. Yu. Zyatkov, A. Yu. Prikhodko, N. M. Prokhoshin, M. A. Shishlenin,
�Mathematical modeling and forecasting of COVID-19 in Moscow and Novosibirsk region�, Sib. Zh. Vychisl. Mat., 23:4
(2020), 395�414.
Challenges of the development of a hardware and software platform for environmental monitoring
and environmental modeling
M. A. Marchenko
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Novosibirsk State University
E-mail: marchenko@sscc.ru
DOI 10.24412/cl-35065-2021-1-03-09
The concept of creating an integrating platform (IP) for collecting and analyzing environmental monitoring
data based on the development of domestic scientific and educational organizations and high-tech companies
is proposed. The software and hardware components of such a platform, which exist at the Institute of Com-
putational Mathematics and Mathematical Geophysics of the SB RAS (ICMMG), are described.
The world practice of environmental monitoring consists in creating networks for monitoring the envi-
ronmental situation using inexpensive sensors based on the Internet of Things (IoT) technology and using arti-
ficial intelligence methods. Objects of monitoring and forecasting of such networks: the layer of the atmos-
phere above the land, sea and coastal zones, aquatic environment (sea and coastal zones, rivers and lakes,
reservoirs).
IP composition:
� a network of sensors and environmental monitoring devices with precise reference to the terrain thanks
to the GIS system,
� software package for assimilation of monitoring data and forecasting based on artificial intelligence
methods.
� supercomputer center (SCC) for data collection and analysis.
Application of IP:
� collection of environmental information,
� forecasting and modeling situations necessary for decision-making,
� assessment of the risks of negative impact of hazardous natural and man-made impacts on the ecosys-
tem, infrastructure and population.
