Computation Model of Cyber-Physical Immunosensor System

• Published in: IEEE access 2019, Vol.7, p.62325-62337
• Main Authors: Martsenyuk, Vasyl, Klos-Witkowska, Aleksandra
• Format: Article
• Language: English
• Subjects: Algorithms; Antibodies; Antigens; Biosensors; Computation; Computer simulation; Convergence; Cyber-physical system; Delay effects; Delays; Differential equations; dynamic logic; Fluorescence; immunosensor; Immunosensors; Initial conditions; Mathematical model; Mathematical models; Maxima; Operators (mathematics); population dynamics; practical stability; Stability analysis; Time lag
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2019.2915946

This paper initiates a study toward developing and applying computation models of cyber-physical immunosensor systems (CPISS). The focus is on the mathematical description of continuous population dynamics combined with dynamic logic used for discrete events. First, we introduce a class of lattice differential equations with time delay simulating antigen-antibody interactions within immunopixels. The spatial operator is modeling diffusion-like interaction between immunopixels. We then use the syntax of dynamic logic to describe discrete states of the immunopixel as a result of fluorescencing. An electrical signal which is simulated as a number of immunopixels' fluorescencing is important from the viewpoint of CPISS design. Stability research is focused on the notion of practical stability. For this purpose, we constructed a specific randomized multivariate algorithm, which provides a probabilistic estimate of the practical stability of the immunosensor system. In particular, we use the Monte Carlo technique. It analyzes both initial conditions and time delay and rate parameters. The experimental results obtained provide a complete analysis of immunosensor model stability with respect to changes of time delay, namely, as the time delay was increased, the stable endemic solution changed at a critical value to a stable limit cycle. Furthermore, when increasing the time delay, the behavior changed from convergence to simple limit cycle to convergence to complicated limit cycles with an increasing number of local maxima and minima per cycle until, at sufficiently high time delay, the behavior became chaotic. Such behavior can be seen using both phase portraits, tile plots, and simulated electrical signal. Mathematical models and algorithms, which are developed in this paper, may be considered as additional skills of CPISS. There is shown their software implementation as methods in language R.