The article is devoted to the analysis and implementation of satellite observations data assimilation and filtration highly technological methods used in the hydrodynamics and biological kinetics of shallow reservoirs mathematical models development and verification. The paper considers the using neural networks possibility and describes various methods for filtering images obtained from satellite earth sensing data. The plankton populations evolution mathematical model in the Azov sea is considered. Its calibration and verification is carried out using observations satellite assimilation methods. The purpose of this work is to create a software tool used at the preliminary and final stages of hydrobiological processes in shallow water mathematical modeling.

This paper considers an integro-differential model of informational confrontation based on Rashevky’s neurological scheme which is difficult to modify for taking into account the differences in susceptibility of individuals to propaganda, the special influence of the reference group for a given individual or the variance of some characteristics of individuals. This can be done by using a discrete model based on a cellular automaton having macrodynamic similar to that of the continuous model. Such a model is proposed in this paper, its dynamics is studied and it is shown to yield the main results, given by the continuous model.

The spread of infectious diseases is a complex phenomenon with many interacting factors. The key role of mathematical epidemiology is to create pathogen spread patterns. These models serve as the mathematical basis for understanding the complex dynamics of the spread of the disease. There are various mathematical models of epidemics, but depending on the type of epidemic, there is a need for their careful analysis and improvement. In 1927, Kermak W. and Mackendrick A. published their theory, on the basis of which the SIR-model (Susceptible-Infected-Removed) was built. This theory was a hypothesis about the spread of an infectious disease among the population. This model has still not lost its relevance and is well suited for predicting the spread of infectious diseases. The aim of the work was to develop and study a mathematical model of the spread of the epidemic based on existing models of epidynamics.
The work investigated the processes of epidemics using the classical SIR model and its modifications: SEIRD models (Susceptible-Exposed-Infected-Removed-Dead) and SEIHFRmodels (Susceptible-Exposed-Infected-Hospitalized-Funeral-Removed). A numerical simulation of the dynamics of the spread of viral disease in various scenarios of its course has been carried out. The modern methods and means of mathematical modeling of the spread of viral diseases have been investigated; analyzed their effectiveness depending on the type of epidemic. New modifications of well-known models based on systems of differential equations that take into account the characteristics of the acquisition of immunity, as well as the effect of delay in detecting infected people, are pro-posed. The sensitivity of the parameters included in the model is investigated.
The results can be used to study the processes of modern epidemics, including the coronavirus pandemic, as well as to effectively predict the dynamics of the disease, to develop effective mechanisms to contain and control epidemics of a local and global nature.

Different ice constructions, such as ice fields, ice ridges, icebergs, are of great interest for the research, for example, in the seismic prospecting works. Ice constructions, especially ice fields, bring in lots of extra reflections into the seismograms, which are very difficult to differ from the reflections, coming from the hydrocarbon deposits, which are of great importance for the geologists. For the decrease of the influence of the reflections from the ice field, the seismic source of impulse is often established deep into the ice cover, approaching the contact border between the ice and the water layer. In this work, the results of mathematical modelling of the seismic waves spread through the geological layers of the Arctic region with the help of the grid-characteristic method are presented. The analysis of influence of establishing the source of impulse on the border between ice and water on the decrease of the seismic wave velocities, on the wave fields is carried out. The model with the seismic source of impulse, located on the contact border between ice and water, makes worse the final result, while the model with the source of impulse on the surface of ice demonstrates a decrease of the seismic wave velocities.

This brief analytical review prepared by I.G. Pospelov summarizes the achievements of a scientific school founded by Academician A.A. Petrov and developed in the works of corresponding members of the RAS: I.G. Pospelov, A.A. Shananina and their colleagues, which occupies a leading position in Russia in the field of prognostic modeling of economic systems and is known in the world scientific community for innovative research.

The multicriteria complex catalytic reactions optimal control based on the kinetic model is relevant for both industrial and laboratory processes. It is necessary to determine the stability radius for each parameter, for the chemical kinetics problems in the analysis of multicriteria optimization stability, with the aim of possible change in the calculated values with a given error.
The multicriteria optimization problem statement (MCO) for the catalytic reaction based on the kinetic model is presented. The solution stability definition of the MCO problem and the stability radius is given.
An algorithm has been developed for calculating the stability radius of the MCO problem solution. The problem of the MCO conditions was solved on the kinetic model basis for the catalytic reaction of primary amines methylation with dimethyl carbonate, and the acceptable range of changes in the optimal temperature and reaction time was calculated to prevent a strong change in the optimality criteria values.
The multicriteria complex catalytic reactions optimal control based on the kinetic model is relevant for both industrial and laboratory processes. However, only the all effective trajectories calculation, the varied parameters values and optimality criteria is insufficient. For the application in practice of the calculated modes for decision makers (DM), information on the acceptable interval for changing the optimal modes is important. In this work, for the catalytic reaction of methylation of primary amines with dimethyl carbonate, the problem of the MCO conditions was carried out on the basis of the kinetic model and the allowable range of changes in the optimal temperature and reaction time was calculated to prevent a strong change in the values of the optimality criteria.

The paper considers the application of the scheme based on linear combination of the Upwind and Standard Leapfrog difference schemes with weight coefficients obtained by minimizing the approximation error. According to the resulting error estimation, it is preferable to use the proposed difference scheme with the approximation error О(ch²) for small Courant numbers than the classical Upwind and Standard Leapfrog difference schemes with the approximation errors О(ch²). The paper presents the comparison solution of the transfer problem based on the proposed scheme with the results obtained using the scheme, which is the linear combination of the Upwind Leapfrog and central difference schemes, as well as two-parameter difference scheme with the third order of accuracy.