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JOURNALS // Matematicheskaya Biologiya i Bioinformatika // Archive

Mat. Biolog. Bioinform., 2025 Volume 20, Issue 2, Pages 644–652 (Mi mbb618)

Mathematical Modeling

The theory of chain processes in biology and sociology

A. A. Filippova, R. A. Filippov-Kuznetsova, A. S. Botinbcd

a N.N. Semenov Federal Research Center for Chemical Physics Russian Academy of Sciences, Moscow
b Peoples' Friendship University of Russia named after Patrice Lumumba, Moscow
c Russian University of Biotechnology (ROSBIOTECH), Moscow, Russia
d Institute of Emergency Medical Care named after N. V. Sklifosovskii, Moscow

Abstract: The theory of numerical growth of living organisms in nature is proposed, in which “active components” transform “neutral components” into new “active centers” as a result of branched, chain processes, according to the autocatalytic equation, and their numerical growth is described by logistic functions. These components and the conditions of their interaction form an “autocatalytic set” that is universal for many processes of numerical growth of various living organisms in nature. Our theory follows from the “theory of chain reactions” and the “mathematical theory of epidemics and pandemics based on the laws of chain and thermal explosions” and can be used to describe the spread of infections among animals and will be useful for describing many processes of growth of wildlife. The theory is likely to make it possible to study many processes of the spread of various “viral ideas” among people, which may be of considerable practical interest in the analysis of social phenomena.

Key words: theory of chain reactions, chain processes, logistic function.

Received 16.11.2025, 28.11.2025, Published 11.12.2025

DOI: 10.17537/2025.20.644



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