Differential equation models of neurodegenerative disease dynamics
*Vikrant PawarCorresponding authorpvikrant8629@gmail.comDepartment of Neuro SurgeryKrishna Institute of Medical SciencesKrishna Vishwa Vidyapeeth (Deemed to be University)Karad, Maharashtra, 415539, IndiaView full profile → , A. K. Bhuvaneswaribhuvaneswari@avit.ac.inDepartment of Humanities and SciencesAarupadai Veedu Institute of TechnologyVinayaka Mission’s Research Foundation (Deemed to be University)Chennai, Tamil Nadu, 603104, IndiaView full profile → , Payal Singhpayal.singh2875@paruluniversity.ac.inDepartment of Applied Sciences and HumanitiesFaculty of Engineering & TechnologyParul UniversityVadodara, Gujarat, 391760, IndiaView full profile → , Lulup Kumar Sahoolulupkumarsahoo@soa.ac.inDepartment of NeurologyInstitute of Medical Sciences & SUM HospitalSiksha ‘O’ Anusandhan (Deemed to be University)Bhubaneswar, Odisha, 751030, IndiaView full profile → , Surayyo Khasanovaxasanova_surayyo@mamunedu.uzDepartment of Psychology and MedicineMamun UniversityKhiva, 220900, UzbekistanView full profile → , Komal Parasharkomal.parashar.orp@chitkara.edu.inCentre of Research Impact and Outcome (CRIO)Chitkara UniversityRajpura, Punjab, 140417, IndiaView full profile → , Yodgor KenjaevDepartment of Basic Medical SciencesTermez University of Economics and ServiceTermez, 190111, UzbekistanView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 27 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2804
- Pages:
- 2865–2878
Abstract
The quantitative prediction of neurodegenerative diseases is difficult because they show progressive loss of neurons that is accompanied by complex interactions between protein aggregation, neuroinflammation, oxidative stress, cellular dysfunction, and others. The aim of this study is to create a nonlinear system of ordinary differential equations (ODEs) to account for the dynamics of the disease, by modelling healthy neurons, damaged neurons, toxic protein accumulation, inflammatory response and therapeutic action. Disease progression under different biological conditions is evaluated by stability analysis, equilibrium analysis, sensitivity analysis and numerical simulation by the fourth order Runge–Kutta method. The results show that the decrease of toxic protein aggregation and inflammatory activity is associated with substantial delay in the process of neuronal degeneration and stability of the system in the long run. The proposed mathematical framework will enable understanding of the evolution of disease, pinpoint influential disease parameters for targeted disease intervention, and provide a predictive tool which can be used for planning individualized therapeutic strategies and future computational neuroscience studies.
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References
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