ライブラリ登録: Guest
Journal of Automation and Information Sciences

年間 12 号発行

ISSN 印刷: 1064-2315

ISSN オンライン: 2163-9337

SJR: 0.173 SNIP: 0.588 CiteScore™:: 2

Indexed in

Approach to the Study of Global Asymptotic Stability of Lattice Differential Equations with Delay for Modeling of Immunosensors

巻 51, 発行 2, 2019, pp. 58-71
DOI: 10.1615/JAutomatInfScien.v51.i2.70
Get accessGet access

要約

Consideration is given to the model of immunosensor based on a system of lattice differential equations with delay. The main result of the work is the conditions for the global asymptotic stability of the endemic state. For this purpose we have used Lyapunov functionals method which combines a general approach to constructing Lyapunov functionals for predator-prey models using lattice differential equations. Calculation of basic reproduction numbers is based on the next generation matrix method. The time delay estimate which provides the global asymptotic stability is presented.

参考
  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, 92, No. 6, 919–923.

  2. Mehrotra P., Biosensors and their applications — a review, Journal of Oral Biology and Craniofacial Research, 2016, 6, No. 2, 153–159. DOI: 10.1016/j.jobcr.2015.12.002. Available: https://doi.org/10.1016/ j.jobcr.2015.12.002

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

  4. Martsenyuk V.P., Klos-Witkowska A., Sverstyuk A.S., Study of classification of immunosensors from viewpoint of medical tasks, Medical informatics and engineering, 2018, No. 1(41), 13–19. DOI: https://dx.doi.org/10.11603/mie.1996-1960.2018.1.8887

  5. Martsenyuk V.P., Andrushchak I.E., Zinko P.N., Sverstiuk A.S., On application of latticed differential equations with a delay for immunosensor modeling, Mezhdunarodnyi nauchno-tekhnicheskiy zhurnal “Ptoblemy upravleniya i informatiki”, 2018, No. 3, 37–45.

  6. Moina C., Ybarra G., Fundamentals and applications of immunosensors, Advances in immunoassay technology, 2012, 65–80.

  7. Martsenyuk V., Klos-Witkowska A., Sverstiuk A., Stability, bifurcation and transition to chaos in a model of immunosensor based on lattice differential equations with delay, Electronic Journal of Qualitative Theory of Differential Equations, 2018(27), 1–31, 2018. DOI: 10.14232/ejqtde.2018.1.27

  8. McCluskey C.C., Complete global stability for an SIR epidemic model with delay — distributed or discrete, Nonlinear Analysis: Real World Applications, 2010, 11, No. 1, 55–59. DOI: 10.1016/ j.nonrwa.2008.10.014. Available: https://doi.org/10.1016/j.nonrwa.2008.10.014

  9. McCluskey C.C., Global stability for an SIR epidemic model with delay and nonlinear incidence, Nonlinear Analysis: Real World Applications, 2010, 11, No. 4, 3106–3109. DOI: 10.1016/j.nonrwa. 2009.11.005. Available: https://doi.org/10.1016/j. nonrwa.2009.11.005

  10. He X.-z., Stability and delays in a predator-prey system, Journal of Mathematical Analysis and Applications, 1996, 198, No. 2, 355–370. DOI: 10.1006/jmaa.1996.0087. Available: https://doi.org/ 10.1006/jmaa.1996.0087

  11. Foryś U., Marchuk’s model of immune system dynamics with application to tumour growth, Journal of Theoretical Medicine, 2002, 4, No. 1, 85–93. DOI: 10.1080/10273660290052151, eprint: http://www.tandfonline.com/doi/pdf/10.1080/10273660290052151

  12. Nakonechny A., Marzeniuk V., Uncertainties in medical processes control, Lecture Notes in Economics and Mathematical Systems, 2006, 581, 185–192, cited By 2. DOI: 10.1007/3-540-35262-7_11

  13. Marzeniuk V., Taking into account delay in the problem of immune protection of organism, Nonlinear Analysis: Real World Applications, 2001, 2, No. 4, 483–496, cited By 2. DOI: 10.1016/ S1468-1218(01)00005-0

  14. Prindle A., Samayoa P., Razinkov I., Danino T., Tsimring L.S., Hasty J., A sensing array of radically coupled genetic “biopixels”, Nature, 2011, 481, No. 7379, 39–44. DOI: 10.1038/nature10722. Available: https://doi.org/10.1038/nature10722

  15. Diekmann O., Heesterbeek J.A.P., Mathematical epidemiology of infectious disease, John Wiley & Son, 2000.

  16. Zhan T., Meng X., Zhang T., Global analysis for a delayed SIV model with direct and environmental transmissions, Journal of Applied Analysis and Computation, 2016. 6(2), 479–491. DOI: 10.11948/ 2016035. Available: http://jaac.ijournal.cn/ch/reader/create_pdf.aspx?file_no=JAAC-V6-2-616& year_id=2016&quarter_id=2

によって引用された
  1. Martsenyuk V., Sverstiuk A., Dzyadevych S. , Identification of parameters and investigation of stability of the mathematical model biosensor for measuring α-chaconine, Scientific journal of the Ternopil national technical university, 96, 4, 2019. Crossref

  2. Марценюк В. П., Карпінські М. , Клос-Витковська А., Весельська О., Андрущак І. Є., Сверстюк А. С., Кучвара О. М., КОМП'ЮТЕРНЕ МОДЕЛЮВАННЯ СПІВІСНУВАННЯ ВІРУСНИХ ШТАМІВ: НЕПЕРЕДБАЧУВАНІСТЬ ЧЕРЕЗ НЕЛІНІЙНІ ЯВИЩА, Medical Informatics and Engineering, 1, 2020. Crossref

  3. Demkovych A. Ye., Yakymchuk M. M., Sverstiuk A. S., Етіологічні фактори ризику виникнення периімплантиту, Clinical Dentistry, 2, 2020. Crossref

Begell Digital Portal Begellデジタルライブラリー 電子書籍 ジャーナル 参考文献と会報 リサーチ集 価格及び購読のポリシー Begell House 連絡先 Language English 中文 Русский Português German French Spain