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Journal of Automation and Information Sciences
SJR: 0.238 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimir: 1064-2315
ISSN On-line: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v51.i2.70
pages 58-71

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

Vasiliy P. Martsenyuk
University of Bielsko-Biala, Poland
Andrey S. Sverstiuk
I. Horbachevsky Ternopol State Medical University, Ternopol
Igor Ye. Andrushchak
Lutsk Technical University, Lutsk


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.


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