Mathematical analysis of complex biological systems using dynamical models
S. PugazhendhiDepartment of PharmacologyMeenakshi College of PharmacyMeenakshi Academy of Higher Education & ResearchChennai, Tamil Nadu, IndiaView full profile → , Neha Rananeha.rana@niu.edu.inSchool of PharmacyNoida International UniversityGreater Noida, Uttar Pradesh, 201312, IndiaView full profile → , *Chidambar JalkuteCorresponding authorDepartment of MicrobiologyKrishna Institute of Science and TechnologyKrishna Vishwa Vidyapeeth (Deemed to be University)Karad, Maharashtra, 415539, IndiaView full profile → , Vikas Dilliwarvikas.dilliwar@rungta.orgDepartment of Computer Science and EngineeringRungta College of Engineering and TechnologyRungta International Skills UniversityBhilai, Chhattisgarh, 490024, IndiaView full profile → , Kapil Mundadakapil.mundada@vit.eduDepartment of Instrumentation EngineeringVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Ayush Gandhiayush.gandhi.orp@chitkara.edu.inCentre for Research Impact and Outcome (CRIO)Chitkara UniversityRajpura, Punjab, 140401, IndiaView full profile → , M. Gayathrigayathrimba@maher.ac.inDepartment of Management StudiesMeenakshi College of Arts and ScienceMeenakshi Academy of Higher Education and ResearchChennai, Tamil Nadu, 600087, IndiaView 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-2822
- Pages:
- 3097–3107
Abstract
The mathematical modelling of biological systems with multiple components provides a systematic solution to the study of the nonlinear interactions, regulatory mechanisms and dynamic behaviours of those multiple components. The aim in this study is to build the approach of dynamical modeling using ordinary differential equations to simulate the fact of time-varying biological populations, molecular concentrations and regulatory processes. The biological assumptions and initial conditions are specified to set realistic constraints on a system, while the nonlinear interaction functions represent feedback, competition, cooperation, saturation and regulatory effects. The obtained differential equation system is analyzed by considering the equilibrium, stability analysis and numerical simulation methods. A proper numerical solution method is used to determine system trajectories for various parameter and initial conditions. The capability of the proposed model to describe steady states, transient responses, oscillatory behaviour and sensitivity to the biological parameters is also illustrated by the simulation results.
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References
[1] P. Kraikivski, “Mathematical modeling in systems biology,” Entropy, vol. 25, no. 10, Art. no. 1380 (2023), doi: 10.3390/e25101380.
[2] R. López-Ruiz, “Mathematical biology: Modeling, analysis, and simulations,” Mathematics, vol. 10, no. 20, Art. no. 3892 (2022), doi: 10.3390/math10203892.
[3] M. Pruthi, A. K. Yadav, and P. Soni, “Quantum synchronizable codes through generalized cyclotomy of order 2r over Z2n,” Journal of Interdisciplinary Mathematics, vol. 29, no. 7, pp. 2205–2216 (2026), doi: 10.47974/JIM-2382.
[4] A. Farea, O. Yli-Harja, and F. Emmert-Streib, “Using physics-informed neural networks for modeling biological and epidemiological dynamical systems,” Mathematics, vol. 13, no. 10, Art. no. 1664 (2025), doi: 10.3390/math13101664.
[5] J. E. Mahbuba and X.-S. Wang, “Stability analysis of biological systems under threshold conditions,” Symmetry, vol. 17, no. 8, Art. no. 1193 (2025), doi: 10.3390/sym17081193.
[6] Y. Chen and M. Frenkel-Morgenstern, “Artificial intelligence research for complex biological systems: Integrating data, models, and biological knowledge,” Biology, vol. 15, no. 14, Art. no. 1137 (2026), doi: 10.3390/biology15141137.
[7] P. Khobragade, G. Gandal, A. Somatkar, H. M. Panchabudhe, P. P. Ashok, and B. Madaminov, “Heat transfer modeling using fractional differential equations,” Journal of Interdisciplinary Mathematics, vol. 29, no. 3, pp. 749–756 (2026).
[8] J. Liu and L. Zhang, “A system dynamics model for simulating the development of postgraduate innovation capacity in smart learning environments,” Mathematics, vol. 14, no. 9, Art. no. 1460 (2026), doi: 10.3390/math14091460.
[9] K. G. Tharunraj and P. Ragukumar, “Log-linear algorithm to generate prime trees,” Journal of Information and Optimization Sciences, vol. 47, no. 7, pp. 2635–2649 (2026), doi: 10.47974/JIOS-2176.
[10] G. Ben-Mizrahi, “AI-driven cyber threat intelligence frameworks for next-generation network security,” Multidisciplinary Journal of Research in Engineering and Technology, vol. 13, no. 2, pp. 55–60 (2026).
[11] A. Lucido, O. Basallo, A. Marin-Sanguino, A. Eleiwa, E. S. Martinez, E. Vilaprinyo, A. Sorribas, and R. Alves, “Multiscale mathematical modeling in systems biology: A framework to boost plant synthetic biology,” Plants, vol. 14, no. 3, Art. no. 470 (2025), doi: 10.3390/plants14030470.
[12] M. Shams, N. Kausar, and I. A. Șomîtcă, “Efficient multiplicative calculus-based iterative scheme for nonlinear engineering applications,” Mathematics, vol. 12, no. 22, Art. no. 3517 (2024), doi: 10.3390/math12223517.
[13] M. Nurmuhammed, O. Akdağ, and T. Karadağ, “Anatolian caracal optimization algorithm: A three-stage hybrid bio- and physics-inspired framework for optimization problems,” Mathematics, vol. 14, no. 16, Art. no. 3007 (2026), doi: 10.3390/math14163007.
[14] R. C. Poonia, R. Almakki, A. K. J. Saudagar, A. Altameem, and M. Albathan, “An optimization approach for real-time object detection in IoT devices through edge computing and deep learning,” Journal of Information and Optimization Sciences, vol. 45, no. 5, pp. 1465–1475 (2024), doi: 10.47974/JIOS-1768.
