Nonlinear Decomposition Principle and Fundamental Matrix Solutions for Dynamic Compartmental Systems
This work provides a novel mathematical framework for analyzing nonlinear compartmental systems, which is relevant for fields like ecology, epidemiology, and pharmacokinetics.
The paper introduces a decomposition principle for nonlinear dynamic compartmental systems, enabling tracking of all initial stocks, external inputs, and intercompartmental flows individually. The method is applied to various models, demonstrating its efficiency and wide applicability.
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning methodologies. A deterministic mathematical method is developed for the dynamic analysis of nonlinear compartmental systems based on the proposed theory. The dynamic method enables tracking the evolution of all initial stocks, external inputs, and arbitrary intercompartmental flows, as well as the associated storages derived from these stocks, inputs, and flows individually and separately within the system. The transient and the dynamic direct, indirect, acyclic, cycling, and transfer (diact) flows and associated storages transmitted along a particular flow path or from one compartment--directly or indirectly--to any other are then analytically characterized, systematically classified, and mathematically formulated. Thus, the dynamic influence of one compartment, in terms of flow and storage transfer, directly or indirectly on any other compartment is ascertained. Consequently, new mathematical system analysis tools are formulated as quantitative system indicators. The proposed mathematical method is then applied to various models from literature to demonstrate its efficiency and wide applicability.