DOI: https://doi.org/10.15588/1607-3274-2019-2-14

COMPUTER MODELING OF CYBER-PHYSICAL IMMUNOSENSOR SYSTEM IN A HEXAGONAL LATTICE USING LATTICE DIFFERENTIAL EQUATIONS WITH DELAY

V. P. Martsenyuk, A. S. Sverstiuk

Abstract

Context. An important stage in the design of cyber-physical immunosensory systems is the development and research of their
mathematical and computer models, the construction of which would be based on biological assumptions to obtain appropriate
systems of differential equations of population dynamics. Mathematical modeling would allow to obtain the value of parameters that
would ensure the operational stability of immunosensory systems.
Objective. The aim of the work is to develop a mathematical and computer model of the cyber-physical immunosensory system
using lattice-delayed differential equations on a hexagonal lattice and study its stability.
Method. The mathematical and computer models of the cyber-physical immunosensory system on the hexagonal lattice are developed.
For the simulation of continuous dynamics, the system of lattice differential equations with delay was used. Dynamic logic
of the first order is used to simulate discrete events. The permanent states of the model as solutions of the corresponding algebraic
systems are described. The conclusion on stability is based on the analysis of the corresponding phase diagrams, lattice images and
signals obtained from the corresponding computer model.
Results. The analysis of the results of numerical simulation of the investigated model in the form of an image of phase planes,
lattice images of the probability of antibody bonds and an electron signal from the converter, which characterizes the number of fluorescing
pixels, is presented.
Conclusions. Mathematical and computer modeling of the cyber-physical immunosensory system was performed. It is established
that its qualitative behavior significantly depends on the time of the immune response. The conclusion on the stability of immunosensors
can be made on the basis of the grid image of the pixels that are fluorescing. An electrical signal, modeled by the number
of fluorescent immunopips, is important in the design of cyber-physiological immunosensory systems and studies of their resilience.
Limit cycle or steady focus determine the appropriate form of immunosensory electrical signal. The experimental results obtained
have made it possible to perform a complete analysis of the stability of the immunosensor model, taking into account the delay
in time.

Keywords

computer simulation; mathematical modeling; cyber-physical system; immunosensory system; biosensor; immunosensor; differential equations with delay; lattice differential equations; stability of the model; hexagonal lattice.

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Copyright (c) 2019 V. P. Martsenyuk, A. S. Sverstiuk