Mathematical modeling of population dynamics using differential equations
Lakhwinder Kaurlakhwinder.kaur@rungta.orgDepartment of Computer Science and EngineeringRungta College of Engineering and TechnologyRungta International Skills UniversityBhilai, Chhattisgarh, 490024, IndiaView full profile → , *K. PrakashCorresponding authorprakashk@presidencyuniversity.inPresidency School of Information SciencePresidency UniversityBangalore, Karnataka, 560119, IndiaView full profile → , Tannmay Guptatannmay.gupta.orp@chitkara.edu.inCentre of Research Impact and Outcome (CRIO)Chitkara UniversityRajpura, Punjab, 140417, IndiaView full profile → , H. D. Raghavendra Prasadp.raghavendra@jainuniversity.ac.inDepartment of Civil EngineeringFaculty of Engineering and TechnologyJAIN (Deemed-to-be University)Bangalore, Karnataka, 562112, IndiaView full profile → , Soatmurod Boykobilovsoatmurod_boyqobilov@tues.uzDepartment of Morphological SciencesTermez University of Economics and ServiceTermez, UzbekistanView full profile → , Ilhamdjan Asamovich Karimdjanovdr.ilhomjon@mail.ruDepartment of Children Diseases in Family MedicineTashkent State Medical UniversityTashkent, 100109, 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-2828
- Pages:
- 3173–3182
Abstract
Population dynamics are used to give a mathematical explanation to changes in biological populations where they grow, compete, are limited by resources and affected by the environment. In this study, a framework for population analysis of temporal behavior is developed in the form of nonlinear governing equations of the form of differential equation. System variables that depend on population, assumptions used in the models, and equilibrium states and stability conditions are systematically formulated to describe long-term system behavior. Various population scenarios are represented by the model parameters and initial conditions. Numerical solution algorithm is used to approximate trajectories of populations for which analytical solutions are hard to come by. The suggested system measures changes in the size of the population, rate of growth, convergence to equilibrium and stability under varying parameter conditions. The examples show how differential equations can be used to model complex interactions in population dynamics and forecast changes in populations over time.
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References
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