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Volume 58 >>> № 4 JULY — AUGUST 2022
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UDC 519.6
S.V. Baranovsky1, A.Ya. Bomba2, S.I. Lyashko3


1 Educational and Scientific Institute of Automatics, Cybernetics, and Computer Engineering of the National University of Water and Environmental Engineering, Rivne, Ukraine

 svbaranovsky@gmail.com

2 Educational and Scientific Institute of Automatics, Cybernetics, and Computer Engineering of the National University of Water and Environmental Engineering, Rivne, Ukraine

 abomba@ukr.net

3 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

 lyashko.serg@gmail.com

GENERALIZATION OF THE ANTIVIRAL IMMUNE RESPONSE MODEL FOR COMPLEX
CONSIDERATION OF DIFFUSION PERTURBATIONS, BODY TEMPERATURE RESPONSE,
AND LOGISTIC ANTIGENS POPULATION DYNAMICS

Abstract. The Marchuk–Petrov mathematical model of antiviral immune response is generalized for complex consideration of diffusion perturbations, concentrated influences, body temperature response, and logistic population dynamics of viral elements and antibodies to the development of infectious disease. A step-by-step procedure for numerically asymptotic solution of the corresponding singularly perturbed problems with delays is developed. The authors present the results of computer simulation, which illustrate the “model” reduction of the maximum level of antigens in the epicenter of infection due to their diffusion “scattering,” body temperature response, and logistic population dynamics of viruses on the nature of infectious disease, including the presence of concentrated sources of antigens. It is emphasized that such a systemic effect of these factors can reduce the initial supercritical concentration of antigens to a level after which their neutralization and excretion will be provided by the existing level of immune protection, which is important in deciding whether to use external “therapeutic” effects.

Keywords: model of antiviral immune response, dynamic systems with delay, asymptotic methods, singularly perturbed problems, concentrated influences, logistics dynamics.


FULL TEXT

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