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Mathematical analysis of Immune Response Dynamics in Parkinson's Disease with Immunotherapeutic Intervention | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 26 اردیبهشت 1405 اصل مقاله (4.25 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.69212.3401 | ||
| نویسندگان | ||
| Sunita Chand؛ Santoshi Panigrahi* | ||
| Department of Mathematics, Siksha `O' Anusandhan (Deemed to be University), Khandagiri Square, Bhubaneswar- 751030, Odisha, India. | ||
| چکیده | ||
| We develop a fractional-order, time-delay mathematical model of Parkinson’s disease that couples neuronal compartments, extracellular α-synuclein, microglial activation and adap tive immune responses. The fractional derivative models long-memory processes (e.g., slow protein aggregation and persistent inflammation) while the discrete delay represents bi ologically observed lags in immune activation. Parameters were estimated by digitizing published time-series, and the fitted model reproduces the qualitative dynamics reported in the literature. We compute the basic reproduction number ℜ0 using the next-generation matrix and perform linear stability and Hopf bifurcation analyses; the first Lyapunov coefficient is negative, indicating a supercritical Hopf bifurcation and the emergence of stable oscillations for sufficiently large delays. Numerical experiments show that increasing the α-synuclein clearance efficacy (ϵ1) reduces ℜ0 and stabilizes the system, whereas microglial and T-cell suppression (ϵ2,ϵ3) mainly attenuate oscillation amplitude. Our results support immunotherapeutic strategies that prioritize clearance of pathological α-synuclein to limit disease progression. | ||
| کلیدواژه‌ها | ||
| Stability and Hopf Bifurcation؛ Basic Reproduction Number؛ Sensitivity Analysis؛ Parameter Estimation؛ Fractional Delay Differential Equation | ||
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آمار تعداد مشاهده مقاله: 84 تعداد دریافت فایل اصل مقاله: 168 |
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