Abstract. This work is the final part of a series of studies devoted to the creation of a hierarchy of basic models of the biokinetics of aseptic inflammation, which represents a mathematical formalization of fundamental general biological concepts about the participation of components of the innate immune system in protective and adaptive reactions in the focus of inflammation. The idea of local spatial uniformity of the modelled process is accepted. The formation of a hierarchy of models is based on the bottom-up principle, which allows you to first focus on a variety of details, and then move on to representing the system in its most general form, i.e. at the level of «major degrees of freedom». The idea of reduction is based solely on general biological considerations reflecting objective data on the role of components of the innate immune system in the functioning of the protective and adaptive mechanism of inflammation.

The sequential reduction resulted in eight basic mathematical models of the biokinetics of inflammation. Each of them has successfully passed the validation procedure using experimental time series that characterize the dynamics of in vivo inflammation in excisional skin wounds in mice and several other living models. It is also shown that the proposed structure of the equations of all models makes it possible to adequately reproduce the functioning of the fundamental mechanism of M1/M2 polarization and reprogramming of macrophages. The robustness of each model is confirmed by an analysis of sensitivity to small perturbations of parameters and a cycle of «diagnostic» checks, which consist in a qualitative assessment of possible changes in the main scenario of an acute inflammatory reaction in the well-known disorders of the leukocyte formula or functions of blood cells.

The study of the dependence on the initial conditions showed that all models have the property of multistability in a biologically significant range of parameter values and solutions of the obtained systems of differential equations, due to which the switching of the inflammation scenario from acute to chronic can be mathematically reproduced.

An important place is assigned to the final stage of reduction, focused on defining the minimal model as a key constructive element, which is common to all mathematical models of the hierarchy and the «carrier» of the multistability property. It is shown how only a few «main» ones can be distinguished from the set of degrees of freedom (in the phase space of states), so that the final result was a biologically justified reduction in the dimension of the phase space of states by more than half while preserving the most significant properties of the most complete model and the real object. In the context of aseptic inflammation, the «main degrees of freedom» can be attributed both a priori and according to mathematical modelling to the quantitative characteristics of subpopulations of blood cells (active platelets) and the innate immune system (neutrophils, macrophages). The results of the reduction procedure indicate that the mathematical idealization adopted in the hierarchy of models supports the following fundamental biological fact: the self-organization of immune cells within the framework of a genetically determined inflammatory program, their adaptation in the microenvironment cannot effectively occur without the cytokine involvement.

The practical significance of the proposed models lies in the fact that they are an effective self-sufficient tool for studying a genetically determined program of cellular and molecular immune response to damage of any etiology, and can also be used as a subsystem in complex multilevel multiphysical models of pathogenesis mechanisms of most human diseases. Applications of the developed mathematical models can include ischemic heart attacks, neurodegenerative and oncological processes, damage caused by mechanical or chemical factors, surgical interventions, i.e. the widest range of general pathological processes, in which the innate immune response is an important pathogenesis factor.

Key words: innate immune response, aseptic inflammation, biokinetics, hierarchy of mathematical models, reduction, minimal model, numerical analysis, multistability, surgical skin wound, chronization of inflammation