Step by Step Perturbation of Discrete Models of Immunology

نویسندگان

چکیده

A number of very different mathematical models are used to predict the response immune system pathogenic microorganisms detected in body and corresponding course viral disease. Usually,such based on assumption that is a homogeneous envi-ronment which all factors evenly distributed.The article presents generalized discrete model Marchuk's infectious disease for complex accounting small diffusion «redistributions», con-centrated effects body's temperature response. The introduction such additional terms into basic significantly complicates orig-inal problem aggravates constructing efficient algorithms numerical solution systems differential equations with de-lays. It noted as result discretization original using an implicit scheme, nonlinear obtained, so-lution must be sought at each time step by iterations. Thus, use classical Runge-Kutta schemes uneconomical from point view calculations.The authors propose step-by-step procedure numerically asymp-totic approximation singularly per-turbed delay, allows combine ad-vantages cost-effectiveness explicit schemes. results computer simulations presented, illus-trate influence diffuse «scattering»of antigens, delays concen-trated sources antigens nature em-phasized action these can lead reduction initially supercritical concentration more acceptable level, important forming rational program decision-making external «therapeutic»effects.

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ژورنال

عنوان ژورنال: Matemati?ne ta komp'ûterne modelûvannâ

سال: 2022

ISSN: ['2308-5878']

DOI: https://doi.org/10.32626/2308-5916.2022-23.5-19