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Discontinuity, Nonlinearity, and Complexity 11(1) (2022) 57--72 | DOI:10.5890/DNC.2022.03.005

Debasmita Mukherjee$^{1,2}$ , Lakshmi Narayan Guin$^1$, Santabrata Chakravarty$^1$

$^1$ Department of Mathematics, Visva-Bharati, Santiniketan, 731235, WB, India

$^2$ Department of Statistics, Sunandan Divatia School of Science, SVKM's NMIMS (Deemed to be) University, Mumbai, 400056, MH, India

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Abstract

A model addressing the phagocytosing process of macrophage ingesting oxidised LDL in atherosclerotic plaque formation is presented in this research manuscript. The biological phenomenon of plaque formation has been exposed here in terms of a reaction-diffusion model system in one spatial dimension (1D) by means of no-flux boundary conditions. The present article is mainly focused with the existence and stability of equilibrium solutions as obtained by the model parameters and interpretation of those results in terms of their potential bio-medical implications. Bifurcation analysis of the model system provides six relevant parameters of significance which are clinically sensible. A careful analysis of the model under submission provides an insight to the inflammatory route involved in the atherosclerotic plaque formation.

Acknowledgments

The authors are thankful to the reviewers for their fruitful comments and suggestions. The authors gratefully acknowledge the financial support by Special Assistance Programme (SAP-III) sponsored by the University Grants Commission (UGC), New Delhi, India (Grant No. F.510/3/DRS-III/2015(SAP-I)).

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