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On the dynamics of matrix models for immune clonal networks

Balinsky, A. A. ORCID:, Gafiychuk, V. V., Kyshakevych, B. Yu. and Prykarpatsky, A. K. 2022. On the dynamics of matrix models for immune clonal networks. Journal of Mathematical Sciences 263 , pp. 198-214. 10.1007/s10958-022-05920-x

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We propose some new matrix models for clonal network dynamics that are typical for simulating various biological clonal-type networks and study their dynamics to stable states. We present a detailed description and deduce the corresponding matrix equations governing the dynamics of immune systems on the basis of the general gradient-type principles that can be inherent to a wide class of real living objects. Clonal networks of special type are modeled by symmetric projector matrix variables, which simultaneously take into account both the asymmetry of mutual interaction and adaptation states that can be realized owing to possible idiotypic clonal suppressions. We perform computer simulations of the model dynamics for some simple cases of relatively low dimension paying special attention to the dynamics of the amounts of activated receptor strings within the clonal network.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Springer
ISSN: 1072-3374
Date of First Compliant Deposit: 21 June 2022
Date of Acceptance: 29 April 2022
Last Modified: 10 Nov 2022 11:27

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