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JOURNALS // Sibirskii Zhurnal Industrial'noi Matematiki // Archive

Sib. Zh. Ind. Mat., 2024 Volume 27, Number 4, Pages 84–98 (Mi sjim1304)

Mathematical foundations of the isobolographic method

V. G. Panov

Institute of Industrial Ecology of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620137 Russia

Abstract: More precise definitions of concepts and constructs used in biomedical sciences are proposed to analyze the joint action of factors using isobolograms. Formal definitions of concepts of zero interaction, scale-equivalent dose—response functions, and zero-interaction manifold are given. A general construction is proposed that formalizes the conditions of applicability and the basic methods for analyzing the combined action using isoboles. Equations of zero interaction manifolds are derived both in the case of scale-equivalent and arbitrary dose—response functions.

Keywords: combined (joint) action of factors, isobole, dose—response function, zero interaction, superadditivity, subadditivity, commutative diagram.

UDC: 51-76:514.124:573.2:615.015.2

Received: 08.11.2022
Revised: 03.09.2024
Accepted: 29.10.2024

DOI: 10.33048/SIBJIM.2024.27.406


 English version:
Journal of Applied and Industrial Mathematics, 2024, 18:4, 801–812


© Steklov Math. Inst. of RAS, 2026