{"id":9848,"date":"2021-12-14T19:37:11","date_gmt":"2021-12-14T17:37:11","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=9848"},"modified":"2022-01-26T14:16:52","modified_gmt":"2022-01-26T12:16:52","slug":"modelyuvannya-fizyko-himichnyh-ta-biologichnyh-proczesiv-dyferenczialnymy-rivnyannyamy","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=9848","title":{"rendered":"\u041c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f \u0444\u0456\u0437\u0438\u043a\u043e-\u0445\u0456\u043c\u0456\u0447\u043d\u0438\u0445 \u0442\u0430 \u0431\u0456\u043e\u043b\u043e\u0433\u0456\u0447\u043d\u0438\u0445 \u043f\u0440\u043e\u0446\u0435\u0441\u0456\u0432 \u0434\u0438\u0444\u0435\u0440\u0435\u043d\u0446\u0456\u0430\u043b\u044c\u043d\u0438\u043c\u0438 \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f\u043c\u0438"},"content":{"rendered":"

<\/p>\n

\u041c\u041e\u0414\u0415\u041b\u042e\u0412\u0410\u041d\u041d\u042f \u0424\u0406\u0417\u0418\u041a\u041e-\u0425\u0406\u041c\u0406\u0427\u041d\u0418\u0425 \u0422\u0410 \u0411\u0406\u041e\u041b\u041e\u0413\u0406\u0427\u041d\u0418\u0425 \u041f\u0420\u041e\u0426\u0415\u0421\u0406\u0412 \u0414\u0418\u0424\u0415\u0420\u0415\u041d\u0426\u0406\u0410\u041b\u042c\u041d\u0418\u041c\u0418 \u0420\u0406\u0412\u041d\u042f\u041d\u041d\u042f\u041c\u0418<\/p>\n

MODELING OF PHYSICOCHEMICAL AND BIOLOGICAL PROCESSES DIFFERENTIAL EQUATIONS<\/p>\n

\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: <\/strong>177-187<\/strong>. \u041d\u043e\u043c\u0435\u0440: \u21165, 2021 (301)<\/strong> \"\"<\/a>
\n\u00a0<\/strong>\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\n\u041c\u0410\u0420\u0426\u0415\u041d\u042e\u041a \u0412.\u041f.
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\nORCID ID: 0000-0001-5622-1038
\ne-mail: vmartsenyuk@ath.bielsko.pl
\n\u0421\u0412\u0415\u0420\u0421\u0422\u042e\u041a \u0410.\u0421.
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u043c\u0435\u0434\u0438\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406.\u042f. \u0413\u043e\u0440\u0431\u0430\u0447\u0435\u0432\u0441\u044c\u043a\u043e\u0433\u043e
\nORCID ID: 0000-0001-8644-0776
\ne-mail: sverstyuk@tdmu.edu.ua
\n\u0411\u0410\u0413\u0420\u0406\u0419-\u0417\u0410\u042f\u0426\u042c \u041e.\u0410.
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u043c\u0435\u0434\u0438\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406.\u042f. \u0413\u043e\u0440\u0431\u0430\u0447\u0435\u0432\u0441\u044c\u043a\u043e\u0433\u043e
\nORCID ID: 0000-0002-5533-3561
\ne-mail: bagrijzayats@tdmu.edu.ua
\n\u041f\u0410\u0412\u041b\u0418\u0428\u0418\u041d \u0410.\u0412.
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u043c\u0435\u0434\u0438\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406.\u042f. \u0413\u043e\u0440\u0431\u0430\u0447\u0435\u0432\u0441\u044c\u043a\u043e\u0433\u043e
\nORCID ID: 0000-0002-5506-7582
\ne-mail: pavlyshynav@tdmu.edu.ua
\n\u0411\u041e\u0419\u041c\u0418\u0421\u0422\u0420\u0423\u041a \u0406.\u0406.
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u043c\u0435\u0434\u0438\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406.\u042f. \u0413\u043e\u0440\u0431\u0430\u0447\u0435\u0432\u0441\u044c\u043a\u043e\u0433\u043e
\nORCID ID: 0000-0003-3343-3104
\ne-mail: boymystruk@tdmu.edu.ua
\nMARTSENYUK VP
\nUniversity of Bielsko-Bia\u0142a, Poland
\nSVERSTIUK AS, BAGRIY-ZAYATS OA, PAVLYSHYN AV, BOYMISTRUK II
\nTernopil National Medical University named after I.Ya. Gorbachevsky
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2021-301-5-177-187<\/a>
\n\u0420\u0435\u0446\u0435\u043d\u0437\u0456\u044f\/Peer review <\/strong>: 08.09.2021\u0440.
\n\u041d\u0430\u0434\u0440\u0443\u043a\u043e\u0432\u0430\u043d\u0430\/Printed :<\/strong> 10.10.2021 \u0440.<\/p>\n

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\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0435 \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f, \u0434\u0438\u0444\u0435\u0440\u0435\u043d\u0446\u0456\u0430\u043b\u044c\u043d\u0456 \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f, \u0444\u0456\u0437\u0438\u043a\u043e-\u0445\u0456\u043c\u0456\u0447\u043d\u0456 \u043f\u0440\u043e\u0446\u0435\u0441\u0438.<\/p>\n

\u00a0<\/strong>\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

The approaches to modeling of physicochemical and biological processes of differential equations are explained in the work. The law of radioactive decay, the law of absorption of ionizing radiation by the environment, the law of reproduction of bacteria, the law of dissolution of medicinal substance from a tablet, chemical reactions of the first and second order, mathematical model G.I. Marchuk are resulted, mathematical model of a cyber-physical immunosensory system on a hexagonal lattice using a system of delayed differential equations. The results of mathematical modeling in the form of the results of numerical modeling of the dynamic logic of the cyber-physical immunosensory system are presented. Phase planes, lattice images of the probability of antigen-antibody binding, images of fluorescent pixels, electrical signal from the transducer, which characterizes the number of fluorescent pixels, were obtained. In order to increase the student\u2019s research interest in the study of natural sciences and improve the level of understanding of educational material in the disciplines “Biophysics with physical methods of analysis” and “Higher Mathematics” it is important to inform students about the latest discoveries in this field of knowledge, modern scientific mathematical and physical schools, because it is largely a motivating factor in the formation of future specialists in medicine, pharmacy, biology. Acquainting students with the current results of their own research allows them to be interested in the process of modeling medical and biological processes using differential equations, motivating them to their own research and development of various biosensor devices.
\nKeywords:<\/strong> mathematical modeling, differential equations, physicochemical processes.<\/p>\n

References<\/strong><\/p>\n

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