УДК 602.1:519.85:53.082.9:616-07

ВИКОРИСТАННЯ ДИФЕРЕНЦІАЛЬНИХ РІВНЯНЬ ІЗ ЗАПІЗНЕННЯМ
НА ГЕКСАГОНАЛЬНІЙ РЕШІТЦІ ДЛЯ МОДЕЛЮВАННЯ ІМУНОСЕНСОРІВ

Марценюк Василий Петрович,
доктор техн. наук, профессор кафедры Университета в Бельско-Бялой, Польша,
 vmartsenyuk@ath.bielsko.pl

Сверстюк Андрей Степанович,
кандидат техн. наук, доцент кафедры Тернопольского государственного медицинского университета им. И.Я. Горбачевского,  sverstyuk@tdmu.edu.ua;  sverstyuk@ukr.net

Гвоздецкая Ирина Степановна,
кандидат техн. наук, доцент кафедры Тернопольского государственного медицинского университета им. И.Я. Горбачевского,  hvozdecka@tdmu.edu.ua

СПИСОК ЛІТЕРАТУРИ

1. Mosinska L., Fabisiak K., Paprocki K., Kowalska M., Popielarski P., Szybowicz M., Stasiak A. et al. Diamond as a transducer material for the production of biosensors. Przemysl Chemiczny. 2013. Vol. 92, N 6. P. 919–923.


2. Mehrotra P. Biosensors and their applications — a review. Journal of Oral Biology and Craniofacial Research. 2016. Vol. 6, N 2. P. 153–159. DOI: https://doi.org/10.1016/j.jobcr.2015.12.002.


3. Kos-Witkowska A. Enzyme-based fluorescent biosensors and their environmental, clinical and industrial applications. Polish Journal of Environmental Studies. 2015. Vol. 24. P. 19– 25. DOI: https://doi.org/10.15244/pjoes/28352.


4. Martsenyuk V.P., Klos-WitkowskaA., Sverstyuk A.S. Study of classification of immunosensors from viewpoint of medical tasks. Medical Informatics and Engineering. 2018. N 1. P. 13–19. DOI: https:// dx.doi.org/10.11603/mie.1996-1960.2018.1.8887.


5. Марценюк В.П., Андрущак И.Е., Зинько П.Н., Сверстюк А.С. Об использовании решетчастых дифференциальных уравнений с запаздыванием для моделирования иммуносенсора. Международный научно-технический журнал «Проблемы управления и информатики». 2018. № 3. С. 37–45.


6. Moina C., Ybarra G. Fundamentals and applications of immunosensors. In: Advances in Immunoassay Technology. Chiu N. (Ed.). 2012. P. 65–80. DOI: https:// dx.doi.org/10.5772/1967.


7. Kos-Witkowska A. The phenomenon of fluorescence in immunosensors. Acta Biochimica Polonica. 2016. Vol. 63, N 2. P. 215–221. DOI: https://doi.org/10.18388/abp.2015_1231.


8. Hexagonal grids. URL: https://www.redblobgames.com/grids/hexagons/.


9. McCluskey C.C. Complete global stability for an SIR epidemic model with delay — distributed or discrete. Nonlinear Analysis: Real World Applications. 2010. Vol. 11, N 1. P. 55–59. DOI: https: //doi.org/10.1016/j.nonrwa.2008.10.014.


10. Nakonechny A., Marzeniuk V. Uncertainties in medical processes control In: Lecture Notes in Economics and Mathematical Systems. 2006. Vol. 581. P. 185–192. DOI: https://doi.org/10.1007/ 3-540-35262-7_11.


11. Marzeniuk V. Taking into account delay in the problem of immune protection of organism. Nonlinear Analysis: Real World Applications. 2001. Vol. 2, N 4. P. 483–496 DOI: https://doi.org/ 10.1016/S1468-1218(01)00005-0.


12. Prindle A., Samayoa P., Razinkov I., Danino T., Tsimring L.S., Hasty J. A sensing array of radically coupled genetic “biopixels”. Nature. 2011. Vol. 481, N 7379. P. 39–44 DOI: https://doi.org/ 10.1038/nature10722.


13. Hale J.K., Lunel S.M.V. Introduction to functional differential equations. In: Applied Mathematical Series. New York : Springer Verlag, 2013. Vol. 99. DOI: https://doi.org/10.1007/978-1-4612-4342-7.


14. Fory U. Marchuk’s model of immune system dynamics with application to tumour growth. Journal of Theoretical Medicine. 2002. Vol. 4, N 1. P. 85–93. DOI: https://doi.org/10.1080/ 10273660290052151.


15. McCluskey C.C. Global stability for an SIR epidemic model with delay and nonlinear incidence. Nonlinear Analysis: Real World Applications. 2010. Vol. 11, N 4. P. 3106–3109. DOI: https:// doi.org/10.1016/j.nonrwa.2009.11.005.


16. He X.-z. Stability and delays in a predator-prey system. Journal of Mathematical Analysis and Applications. 1996. Vol. 198, N 2. P. 355–370. DOI: https://doi.org/10.1006/jmaa.1996.0087.


17. Martsenyuk V.P., Andrushchak I.Y., Gvozdetska I.S. Qualitative analysis of the antineoplastic immunity system on the basis of a decision tree. Cybernetics and Systems Analysis. 2015. Vol. 51, N 3. P. 461–470. DOI: https://doi.org/10.1007/s10559-015-9737-6.


18. Martsenyuk V.P., Gandzyuk N.M. Stability estimation method for compartmental models with delay. Cybernetics and Systems Analysis. 2013. Vol. 49, N 1. P. 81–85. DOI: https://doi.org/10.1007/ s10559-013-9488-1.


19. Martsenyuk V.P., Andruschchak I.Ye., Gvozdetska I.S. Estimating the solutions in the model of antitumor immunity with impulsive disturbance. Cybernetics and Systems Analysis. 2012. Vol. 48, N 2. P. 200–204. DOI: https://doi.org/10.1007/s10559-012-9398-7.


20. Martsenyuk V.P., Gvozdetska I.S. On the existence and stability of periodic solutions in the absence of immunity in an impulsive model based on gompertzian dynamics. Cybernetics and Systems Analysis. 2012. Vol. 48, N 4. P. 586–591. DOI: https://doi.org/10.1007/s10559-012-9438-3.


21. Akimenko V., Anguelov R. Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay. Journal of Biological Dynamics. 2017. Vol 11, N 1. P. 75–101. DOI: https://doi.org/10.1080/17513758.2016.1236988.