Mathematical modeling of epidemic spread using nonlinear dynamical systems
Tanveer Ahmad Wanitanveer.ahmad@niu.edu.inDepartment of PhysicsNoida International UniversityGreater Noida, Uttar Pradesh, 201312, IndiaView full profile → , *Satish V. KakadeCorresponding authorsatishvkakade@yahoo.co.inDepartment of Community MedicineKrishna Institute of Medical SciencesKrishna Vishwa Vidyapeeth (Deemed to be University)Karad, Maharashtra, 415539, IndiaView full profile → , Manjusha Tomarmanjushapanwar@gmail.comDepartment of MathematicsIndira College of Engineering & ManagementPune, Maharashtra, 410506, IndiaView full profile → , Sanjay G. Sakharwadesanjay.sakharwade@rungta.orgDepartment of Computer Science and EngineeringRungta College of Engineering and TechnologyRungta International Skills UniversityBhilai, Chhattisgarh, 490024, IndiaView full profile → , Mridula Guptamridula.gupta.orp@chitkara.edju.inCentre for Research Impact and Outcome (CRIO)Chitkara UniversityRajpura, Punjab, 140401, IndiaView full profile → , M. Raghavendraraghavendra1797@vardhaman.orgDepartment of Computer Science and EngineeringVardhaman College of EngineeringHyderabad, Telangana, 501218, IndiaView full profile → , A. Saravanansaravanan.a@adityauniversity.inDepartment of Mechanical EngineeringAditya UniversitySurampalem, Andhra Pradesh, 533437, 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-2835
- Pages:
- 3257–3268
Abstract
The spread of an epidemic is a complex nonlinear process that is affected by the process of transmission, the process of recovery, the interaction of the population and the temporal variation in the epidemiological parameters. This study aims to develop mathematical framework for the modelling of the dynamics of epidemics with the help of non-linear dynamics. The population is broken up into epidemiological compartments and the dynamics of the disease spread and recovery are represented by a set of nonlinear differential equations. The framework proposed analyzes the behavior of infection growth, the peak of an epidemic, the recovery pattern, the equilibrium behavior and the stability of the system for varying parameters. The simulation results show that the nonlinear modelling is a powerful tool to capture epidemic dynamics and gain quantitative understanding of transmission dynamics, assessing control strategies, and making epidemic management decisions.
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References
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