Issue 4 (190), article 4


Kibern. vyčisl. teh., 2017, Issue 4 (190), pp.

Antomonov M.Y.1, D. Biol. Sci., Professor,
Chief Researcher, Laboratory of Epidemiological Research and Medical Informatics
Shevchenko A.A.2, Professor,
Head of Research Center of State University “Dnipropetrovsk Medical Academy of Ministry of Health of Ukraine”
Kulagin A.A.3, Ph.D (Med. Sci.),
Professor of the Department of Hygiene and Ecology
1O.M. Marzeev Institute for Public Health, NAMS of Ukraine,
Ukraine, 02660 Kyiv-94, Popudrenko Str.
2Research Center of State University “Dnipropetrovsk Medical Academy of Ministry of Health of Ukraine”,
Ukraine, 49027, Dnipro, Vernadsky Str., 9
3Dnipropetrovsk Medical Academy of the Ministry of Health of Ukraine
Ukraine, 49027, Dnipro, Soborna Square, 4


Introduction. One of the most urgent problems of environmental health is soil contamination by oil and petroleum products (PP) and its impact on crop productivity and population health. The main task here is to determine the acceptable or safe concentrations of PP in the soil. However, at present time there is no unified approach of PP regulating in different countries. One possible solution of the problem is mathematical modeling of the results of experimental studies. With the help of mathematical models, it becomes possible not only to describe the investigated dependencies, but also to calculate safe levels of PP in the soil.
The purpose of the paper is to develop a methodology for constructing and using multifactor nonlinear regression models from data obtained in a real ecological and biological experiment.
Results. The article presents the results of an experimental study of the influence of one type of petroleum products — diesel fuel, when it enters the soil to germinate one of the most important crops — wheat. It is shown that the mathematical model describing the suppression of wheat growth should be a multifactorial function (“time — concentration — effect”), which has a nonlinear character. An algorithm for constructing multifactorial nonlinear regression models is proposed. On the basis of experimental data, an adequate multifactor nonlinear mathematical model was developed. This made it possible to calculate the threshold concentration of diesel fuel, which does not affect the growth of wheat.
Conclusion. On the basis of the proposed algorithm from experimental data an adequate multifactor nonlinear regression model was constructed. With the help of this model, the concentration of diesel fuel that does not cause a negative effect on the growth of wheat was calculated.
Keywords: petrolproducts, environmental contamination, threshold concentration, mathematical modeling, nonlinear multifactor regression models.

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Reseived 01.08.2017

Issue 185, article 7


KVT, 2016, Issue 185, pp.77-89

UDC 519.876.5:615.33


Antomonov M.Y., Romanenko L.I.

Marzeev’s Public Health Institute of the National Medical Academy of Science of Ukraine of Ukraine, Kiev, Ukraine ,

Introduction. The creation of combined drugs, which are used in the composition of nanoparticles (NPs) is actively developing. The most relevant developments include the NPs composition and antibiotics. Mathematical models of the process under investigation lead to a theoretical understanding of this phenomenon, allow us to describe the process in the form of mathematical functions, make it possible to predict the outcome, to analyze the properties of the model and to obtain new data, without undue experimentation.

The purpose of the article is to determine the characteristics of antimicrobial activity of Ag NP in combination with an antibiotic “Cefazolin” with the help of mathematical models of their actions (“concentration – time – effect”).

Results. Antimicrobial properties of the composite material were considered, which is called the “Silver Shield-1000”, and which consists of antibiotic “Cefazolin” and NPs Ag. Isolated action “Silver Shield-1000” was considered at the first stage of the experiment. For this purpose dilution nanosilver 15,0; 7,5; 3,75; 1,875 (g/cm3), and the holding time was 5, 60, 120, 180 minutes. Based on experimental plots and the general theoretical ideas about the dynamics of the process of the withering away of microbes, mathematical model, y(t) has been selected as the exponential function y = y0 (C) exp[-α(C) T]. The values of the model parameters were calculated based on the original data using numerical methods (Levenberg-Marquardt) and software STATISTICA 10,0. The final model organisms, dying under the influence of the “Silver Shield-1000” had the following form: y = y0 exp(-btC)= 59,74exp(-0,0013 TС). Using this model, the expected value of the concentration С* at which should occur almost complete disappearance of microorganisms immediately after the start of the exposure (С* = 73,15 g/cm3) was calculated. An additional experiment was performed, which confirmed this value that verifies the adequacy of the model as a whole. In the second phase of researching it was experimentally investigated the combined effect of “Silver Shield” — 1000 (3.75 g/cm3) and the antibiotic “Cefazolin” on the death of microorganisms. A mathematical model “concentration — time — effect” for the composite: y = 60,098exp(-0,118 TC) and an antibiotic: y = 60,098exp(-0,012 TC). This made it possible to calculate the efficiency of the composite action compared with isolated action of an antibiotic (k = 9.72). Furthermore, it was shown that the composite exhibits have a much greater effect than the sum of the isolated antibiotic action “Cefazolin” and “Silver shield —1000”. It is possible to determine the nature of such action as potentiation.

Conclusion. Mathematical modeling of the results of an experimental study of the antimicrobial activity of the antibiotic “Cefazolin” in combination with nanoparticles of silver allowed the calculation of the quantitative characteristics of the effectiveness of the active ingredients and performed a meaningful forecast of their action.

Keywords: silver nanoparticles, antibiotic “Cefazolin”, death of microorganisms, mathematical model.

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Received 16.06.16

Issue 182, article 6


Kibern. vyčisl. teh., 2015, Issue 182, pp.

Antomonov M.Y.

State Institution “O.N. Marzeev Institute for Hygiene and Medical Ecology
of NAMS of Ukraine” (Kiev)


Introduction. Modern approaches for data analysis combine classical methods and focused on their practical application. Sometimes the information is presented in the form of qualitative characteristics that are characterize the contamination of the research object. Such binary variables are easily transformed into a probability (in percent), so the task description of results performed using probability theory.
The purpose of the article is to develop such a common method forcalculation joint action of the factors that would allow to operate with qualitative (binary) information and would use techniques and formulas of probability theory
Results. A careful analysis was carried out for the existing approaches in the medical and environmental studies for calculating the effect of the joint action of the factors. It was evaluated disadvantages of these approaches that implemented in the theory of probability and mathematical statistics. The article proposes an original method of calculating the combined effect of the factors that allows you to work with the information expressed in binary form. The final expression was designed by using approach of formal logic and probability theory.
Conclusions. It is shown that the known methods of probability theory cannot be adequately used to evaluate the combined effect of the factors. The original method of calculating the probability of the joint action of factors that take into account their possible connection is described.
Keywords: qualitative data, binary variables, joint effect of the factors, the probability of independent and interdependent events.

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Received 02.06.2015

ISSUE 179, article 7


Kibern. vyčisl. teh., 2015, Issue 179, pp 81-92.

Pashinskaia Svetlana L., Junior researcher of the Medical Informatics Department of the Marzeev’s Institute of Hygiene and Medical Ecology of the National Medical Academy of Sciences of Ukraine, Popudrenko st., 50, Kiev, 02094, Ukraine, email:

Antomonov Mikhail Yu., Dr (Biology), Prof., Head of Medical Informatics Department of Marzeev’s Institute of Hygiene and Medical Ecology of the National Medical Academy of Sciences of Ukraine, Popudrenko st., 50. Kiev, 02094, Ukraine, email:


Introduction. Integrated assessment of environmental quality in medical ecological research used different mathematical structures that are often weighted sum of expression of all reported hazards. The problem of optimal formation of integrated indicators is the direct problem of integral evaluation.

The purpose of paper is to develop methods, algorithms, computational formulas and software implementation for solving the inverse problem of the integral evaluation — identifying destabilizing factors in the assessment of ecological and hygienic objects.

Results. Realization of this aim requires the formulation and solution of problems phased: express processing of data array; the selection of informative features; construction of an integrated evaluation.

Algorithm of construction integrated evaluation is implemented as follows: the calculation of the normalized equivalents of selected indicators; calculation of weighted average grade of the objects on the normalized equivalents; calculation shifted integrated evaluation, as the square root of the product of the minimum and weighted average; comparison of average and shifted integrated evaluation; identification of critical elements.

The paper presents an automated technology analysis and evaluation of the primary indicators in order to optimize their list to calculate the integral evaluation. The technology allows working with arrays having outliers and missing data. We consider a phased construction of an integrated assessment. The nonlinear algorithm of integration indicator formation and the method for identifying critical elements were developed.

Conclusions. The proposed technology allows to quickly implementing the processing of the data array, to bring it to a format suitable for further, more detailed analysis and to form an integrated assessment. The results of processing may be performed within the environmental and medical objects; identify objects with the most adverse environmental conditions and disease. Calculation of displaced integral indicators shows destabilizing elements in the system of indicators.

Keywords: integrated evaluation, ecological and hygienic objects, medical and ecological research.

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Received 07.11.2014