A mathematical model of the glucocorticoid effects following preventive administration in a model of neuroinflammation

Elena Lebedeva; Ekaterina Kukushkina; Marina Karpenko; Elena Lebedeva; Ekaterina Kukushkina; Marina Karpenko

doi:10.3934/biophy.2026019

AIMS Biophysics

2026, Volume 13, Issue 3: 328-367. doi: 10.3934/biophy.2026019

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Research article

A mathematical model of the glucocorticoid effects following preventive administration in a model of neuroinflammation

1.
Peter the Great St. Petersburg Polytechnic University, Saint Petersburg, Russia
2.
Laboratory of Neurochemistry, Pavlov Department of Physiology, Institute of Experimental Medicine, St. Petersburg, 197022, Russia

Received: 30 June 2026 Revised: 22 August 2026 Accepted: 01 September 2026 Published: 09 September 2026

A mathematical model of neuroinflammation is proposed that describes the interplay among the peripheral inflammatory response, microglial activation, neural tissue damage, changes in blood–brain barrier permeability, and the effects of preventive glucocorticoid administration. The model is formulated as a system of ordinary differential equations and is intended to investigate the conditions governing the transition from an acute inflammatory response to a stable chronic state. The analysis includes verification of the models' well-posedness, identification of equilibria, local stability analysis, bifurcation analysis, and parameter sensitivity analysis. Three dynamic regimes were identified: rapid resolution of inflammation, delayed recovery accompanied by persistent changes in the central nervous system, and transition to chronic neuroinflammation. The development of chronic neuroinflammation was shown to be associated with strengthening of the positive feedback circuit between central inflammatory mediators and activated microglia. The parameters exerting the greatest influence on the duration of the inflammatory response, accumulation of neural tissue damage, and decline in the effectiveness of glucocorticoid-mediated regulation were identified. The model may be used to interpret experimental data, assess the contributions of individual components of the inflammatory response, and investigate the conditions underlying the development of chronic neuroinflammation.
- mathematical modeling,
- ordinary differential equations,
- neuroinflammation,
- glucocorticoids,
- bifurcation analysis
Citation: Elena Lebedeva, Ekaterina Kukushkina, Marina Karpenko. A mathematical model of the glucocorticoid effects following preventive administration in a model of neuroinflammation[J]. AIMS Biophysics, 2026, 13(3): 328-367. doi: 10.3934/biophy.2026019

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Abstract

A mathematical model of neuroinflammation is proposed that describes the interplay among the peripheral inflammatory response, microglial activation, neural tissue damage, changes in blood–brain barrier permeability, and the effects of preventive glucocorticoid administration. The model is formulated as a system of ordinary differential equations and is intended to investigate the conditions governing the transition from an acute inflammatory response to a stable chronic state. The analysis includes verification of the models' well-posedness, identification of equilibria, local stability analysis, bifurcation analysis, and parameter sensitivity analysis. Three dynamic regimes were identified: rapid resolution of inflammation, delayed recovery accompanied by persistent changes in the central nervous system, and transition to chronic neuroinflammation. The development of chronic neuroinflammation was shown to be associated with strengthening of the positive feedback circuit between central inflammatory mediators and activated microglia. The parameters exerting the greatest influence on the duration of the inflammatory response, accumulation of neural tissue damage, and decline in the effectiveness of glucocorticoid-mediated regulation were identified. The model may be used to interpret experimental data, assess the contributions of individual components of the inflammatory response, and investigate the conditions underlying the development of chronic neuroinflammation.

Conflict of interest

The authors declare no conflict of interest.

Author contributions

Elena Lebedeva: methodology, validation, investigation, writing-original draft. Ekaterina Kukushkina: conceptualization, methodology, writing-review and editing. Marina Karpenko: conceptualization, supervision, writing-review and editing. All authors have read and approved the final version of the manuscript.

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