RESEARCH OF PHASE PLANES OF IMMUNOSENSOR MODEL ON A RECTANGULAR LATTICE USING THE DIFFERENTIAL EQUATIONS WITH DELAY IN THE R PACKAGE

Authors

  • Василь Петрович Марценюк University in Belsko Biala, Poland
  • Андрій Степанович Сверстюк I. Horbachevsky Ternopil National Medical University, Ukraine
  • Наталія Василівна Козодій Ternopil National Technical University Ivan Pul'uj, Ukraine
  • Євген Олександрович Давиденко Petro Mohyla Black Sea National University, Ukraine https://orcid.org/0000-0002-0547-3689

DOI:

https://doi.org/10.24025/2306-4412.2.2019.172004

Keywords:

biosensor, immunosensor, mathematical model, differential equations, packet R.

Abstract

The computer simulation of an immunosensor on a rectangular lattice using the differential equations with delay in the R package is carried out in the work. The phase planes of the immunosensor model on the rectangular lattice using the differential equations with delay are investigated, the parameters of the model, their numerical values, as well as the parameters in the R package are presented. The latest researches in the field of immunosensors, their types, and popularity of scientific directions of research during the last five years are analyzed. Despite the huge variety of modern physico-chemical methods for detecting the analytical signal in immunoassay, electrochemical methods with a number of undeniable advantages, such as: high sensitivity and accuracy, selectivity and expressiveness, not high cost and versatility, are in the lead. The R package is described as a programming environment for statistical analysis of data with given values of parameters of the immunosensor model on the rectangular lattice using differential equations with delay. The links to useful sites, referral lists and documentation on the installation and inception of the R package are presented. The results of numerical immunosensor simulation on a rectangular lattice in the form of phase planes make it possible to study the stability of the immunosensor model. In this work, the phase planes of the model of the immunosensor system on the rectangular lattice using differential equations with the help of R package are investigated. The results obtained are crucial in the study of the stability of the immunosensor model. This takes into account the presence of colonies of antigens and antibodies localized in pixels, as well as the diffusion of antigen colonies between pixels. The mathematical description of the immunosensor contains discrete population dynamics, which is combined with the dynamic logic used for discrete events.

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V. P. Martsenyuk, I. E. Andrushchak, P. N. Zynko, and A. S. Sverstiuk, "On the use of lattice differential equations with a delay for modeling an immunosensor", Problemy upravleniya i informatiki, no. 3, pp. 37-45, 2018 [in Russian].

V. P. Martsenyuk, and A. S. Sverstiuk, "Immunosensor model based on lattice differential equations with delay", Shtuchnyy intelekt, no. 1, pp. 42-47, 2018 [in Ukrainian]. [19] V. P. Martsenyuk, A. S. Sverstiuk, and I. E. Andrushchak, "Approach to the study of the global asymptotic stability of lattice differential equations with delay for modeling immunosensors", Problemy upravleniya i informatiki, no. 1, pp. 62-74, 2019 [in Russian].

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Published

2019-10-03

How to Cite

Марценюк, В. П., Сверстюк, А. С., Козодій, Н. В., & Давиденко, Є. О. (2019). RESEARCH OF PHASE PLANES OF IMMUNOSENSOR MODEL ON A RECTANGULAR LATTICE USING THE DIFFERENTIAL EQUATIONS WITH DELAY IN THE R PACKAGE. Bulletin of Cherkasy State Technological University, (2), 37–47. https://doi.org/10.24025/2306-4412.2.2019.172004

Issue

No. 2 (2019)

Section

Automation and Instrumentation

URN

http://vtn.chdtu.edu.uaurn:2306:44552.2019.172004

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Copyright (c) 2020 Василь Петрович Марценюк, Андрій Степанович Сверстюк, Наталія Василівна Козодій, Євген Олександрович Давиденко The authors who publish in this journal agree to the following terms:

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