UDC 519.6
1 Institute of Automatics, Cybernetics, and Computer Engineering of the National University of Water and Environmental Engineering, Rivne, Ukraine
 svbaranovsky@gmail.com
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2 Institute of Automatics, Cybernetics, and Computer Engineering of the National University of Water and Environmental Engineering, Rivne, Ukraine
abomba@ukr.net
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GENERALIZATION OF THE INFECTIOUS DISEASE MODEL TO ACCOUNT FOR SORPTION
THERAPY IN CONDITIONS OF DIFFUSION DISORDERS
Abstract. A mathematical model of the dynamics of a viral infection under the conditions of adsorption therapy, taking into account diffusion perturbations, was formed by generalizing the basic model of an infectious disease using the ideas of modeling adsorption mass transfer processes and perturbation theory. Based on the synthesis of a step-by-step procedure, asymptotic and numerical methods, a computing technology is proposed that provides a stepwise approximation of the solution of a model singularly perturbed problem with a delay as a perturbation of the solution of the corresponding degenerate problem without a delay. The results of the computer modeling illustrate the predictive contribution of the adsorption therapy to the process of neutralization of viral elements in the body. It is noted that the efficiency of the adsorbents will be determined, in particular, by the time of their introduction, which is important to consider when making a decision on the use of appropriate additional therapy in the treatment program.
Keywords: infectious disease model, sorption therapy, dynamic systems with delay, asymptotic methods, singularly perturbed problems, concentrated influences.
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