## Issue 4 (190), article 4

DOI:https://doi.org/10.15407/kvt190.04.056

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

e-mail: antomonov@ukr.net

Shevchenko A.A.^{2}, Professor,

Head of Research Center of State University “Dnipropetrovsk Medical Academy of Ministry of Health of Ukraine”

e-mail: toxysan@ukr.net

Kulagin A.A.^{3}, Ph.D (Med. Sci.),

Professor of the Department of Hygiene and Ecology

e-mail: kulagin111188@ukr.net

^{1}**O.M. Marzeev Institute for Public Health, NAMS of Ukraine**,

Ukraine, 02660 Kyiv-94, Popudrenko Str.

^{2}**Research Center of State University “Dnipropetrovsk Medical Academy of Ministry of Health of Ukraine”**,

Ukraine, 49027, Dnipro, Vernadsky Str., 9

^{3}**Dnipropetrovsk Medical Academy of the Ministry of Health of Ukraine**

Ukraine, 49027, Dnipro, Soborna Square, 4

**ALGORITHMS OF MULTIFACTORIAL REGRESSION MODELING IN ECOLOGICAL AND HYGIENIC STUDIES**

**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.*

REFERENCES

- Tyuleneva V.A. Regarding oil filtration in soils / V.A. Tyuleneva, V.A. Solyanik,

I.V. Vaskina, VS Shalugin // Bulletin of the KSPU. Issue 2. Part 2. 2006. — P. 110–112. (in Russian). - Rogozina E.A. Topical issues on cleaning of oil-contaminated soils / E.A. Rogozina // Oil and Gas Geology. Theory and practice (1). 2006. — pp. 1–10. (in Russian).
- Bilonenko G.M. Changes in soil fertility under hydrocarbon contamination /

G.M. Bilonenko // Bulletin of Agrarian Science. 2002 — No. 10 — P. 52–54.

(in Ukrainian). - Abramov Yu.A. Emergency monitoring / Yu.A. Abramov, E.N. Grinchenko,

A.Yu. Kirochkin and other // X: AGZU. 2005. — p. 530. (in Ukrainian). - Boychenko S.V. Rational use of hydrocarbon fuels / S.V. Boychenko // Monograph. — M.: NAU. 2001. — P. 216. (in Ukrainian).
- Oborin A.A. Oil-contaminated biogeocinoses / A.A. Oborin // Monograph. – Ural Branch of the Russian Academy of Sciences. — Perm: Izvestia Perm. State Tech University 2008. — p. 511. (in Russian).
- Shevchenko A.A. The Study of petroleum stability of Petroleum Products in black-soil / A.A. Shevchenko, A.A. Kulagin // Materials of a Scientific-Practical Conference with International Participation [“Preventive Medicine: Achieving the Present and Looking to the Future”], Dnipropetrovsk, May 19–20, 2016). — Dnipropetrovsk, 2016. —

P. 189–190. (in Ukrainian). - Solntseva N.P. Oil production and geochemistry of natural landscapes / N.P. Solntseva // M., MTU. 1998. — p. 405. (in Russian).
- On approval of maximum permissible concentrations of petroleum products in land (including soils) for various land categories / Ministry of Health of the Republic of Belarus. 2012. — No. 17/1. (in Russian).
- Measures to rehabilitate soils contaminated by oil and petroleum products should be designated concerning sanitary and hygienic norms and environmental conditions assessment [Electronic resource] Access mode: http://ekologprom.com/osnovi-prirodooblastuvannya-ta-zaxistu-navkolishnogo- seredovishha / 92-zaxodi-z-rekultivacii-gruntiv-zabrudnenix-naftoyu.html. (in Ukrainian).
- Procedure for determining the size of damage from pollution of land with chemical substances (approved by Roskomzem on November 10, 1993 and the Ministry of Natural Resources of the Russian Federation on November 18, 1993). (in Russian).
- Methodology of damage determination caused by pollution and clogging of land resources in consequence of violations of environmental legislation / Ministry of Environmental Protection and Nuclear Safety, Kyiv, 1998. (in Ukrainian).
- Goncharuk E.I. Hygienic valuation of chemical substances in soil / E.I. Goncharuk,

I.G. Sidorenko – M.: “Medicine” 1986, — 320 p. (in Russian). - Use of odds ratio or relative risk to measure a treatment effect in clinical trials with multiple correlated binary outcomes: data from NINDS t-PA stroke trial M. Lu,

B.C. Tilley // Statist. Med., 2001. — Vol.20 — P. 1891–1901. doi: 10.1002 / sim.841 - Stability analysis and optimal control of a hand-foot-mouth disease (HFMD) model / Jun-Yuan Yang, Yuming Chen, Feng-Qin Zhang // Journal of Applied Mathematics and Computing. — 2013. — Vol. 41 — T. 1-2. — P. 99–117
- Analysis of a time-delayed mathematical model for solid avascular tumor growth under the action of external inhibitors / Shihe Xu, Yinhui Chen, Meng Bai // Journal of

Applied Mathematics and Computing. — 2016. — Vol. 52. — T. — p. 403–415. - The Foundations of a Unified Approach to Mathematical Modeling of Angiogenesis /

M. Hubbard, P. F. Jones, B. D. Sleeman // International Journal of Advances in Engineering Sciences and Applied Mathematics. — 2009–1: 43. - Optimal control of mathematical models for radiotherapy of gliomas: the scalar case. /

E. Fernández-Cara, L. Prouvée // Computational and Applied Mathematics. — 2016. Vol. 69 — P 1–18. - Introduction to the Use of Regression Models in Epidemiology Ralf Bender, Cancer Epidemiology, v1, 2009, pp. 179–195.
- Qualitative analysis of a SIR epidemic model with a saturated treatment rate / Zhang Zhonghua, Suo Yaohong // Journal of Applied Mathematics and Computing. 2010 34,

T. 1–2, P. 177–194. - Regression models for multiple outcomes in large epidemiological studies. S. B. Bull. // static Med., 1998. — Vol. 17. P. 2179–2197.
- Stochastic Analysis of an Influenza Epidemic Model. / M. Waleed, M. Imran, A. Khan // International Journal of Applied and Computational Mathematics. — 2017 — Vol. 3. —T.2. — P. 425–443.
- A nonlinear population model of diabetes mellitus / A. Boutayeb, A. Chetouani,

A. Achouyab, E. H. Twizell // Journal of Applied Mathematics and Computing, 2006 —Vol. 21. — t 1–2. — p. 127–139. - Biostatistics for Medical and Biomedical Practitioners, 1st Edition / J. Hoffman //

Academic Press, 2015 — 770p. - Biomedical Informatics. Computer Application in Health Care and Biomedicine, 4th edition / Editors: E. H. Shortliffe, J. J. Cimino // NY, Springer, 2014, 965 p.
- Computational and Statistical Methods for Analyzing Big Data with Applications in 1st Edition / S. L. James, M. Zongyuan, G. Y. Xie // Academic Press / — 2015. — 206 p.
- Theory and Methods of Statistics .1st Edition. / P.K. Bhattacharya, P. Burman // Academic Press. — 2016. — 544 p.
- Methodological recommendations for the hygienic substantiation of the MPC of chemical substances in soil No. 2609-82. — (Effective from 05.08.1982). — Moscow: Ministry of Foreign Affairs of the USSR, 1982. — 57 p. (in Russian).

Reseived 01.08.2017