Differential equation models for tumor growth dynamics
Pallavi Vilas Mhaskepallavi.mhaske@mituniversity.edu.inMIT School of Food TechnologyFaculty of MIT ArtMIT Art Design and Technology UniversityPune, Maharashtra, 412201, IndiaView full profile → , Namrata Gawandenamrata.gawande@pccoepune.orgDepartment of Computer EngineeringPimpri Chinchwad College of EngineeringNigdi, Pune, Maharashtra, 411044, IndiaView full profile → , *Mehru Salahuddin TahsildarCorresponding authormehrutahsildar@gmail.comDepartment of PathologyKrishna Institute of Medical SciencesKrishna Vishwa Vidyapeeth (Deemed to be University)Karad, Maharashtra, 415539, IndiaView full profile → , Rahuk Kumar Singhrahul.singh1@niu.edu.inSchool of Engineering and TechnologyNoida International UniversityGreater Noida, Uttar Pradesh, 201312, IndiaView full profile → , Jyotsna Suryavanshijyotsna.suryavanshi@vit.eduDepartment of Engineering Science and HumanitiesVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , P. Sumasreepitasumasree0804@gmail.comDepartment of Computer ScienceAditya Degree & PG College (Autonomous)Kakinada, Andhra Pradesh, 533003, IndiaView full profile → , Indresh Yadavindresh.yadav@gla.ac.inDepartment of Electrical EngineeringGLA UniversityMathura, Uttar Pradesh, 281406, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 27 Apr 2026
- Published Online:
- 27 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2824
- Pages:
- 3123–3134
Abstract
Growth of tumors is a complex process that is regulated by cellular proliferation, the availability of nutrients and the development of blood vessels, as well as by the tumor’s environment. This research builds a mathematical model based on differential equations to analyze the dynamics of tumor growth and the related control of tumor angiogenesis. Proposed model represents tumour cell population and carrying capacity by coupled non-linear differential equations along with the intrinsic proliferation, growth limitation, vascular support and tumour-induced angiogenesis. Systematically biological assumptions and model variables are expressed to set up realistic relations between the expansion of the tumor and the availability of resources. A numerical solution algorithm is used to explore the changes in tumor volume and vascular carrying capacity for various parameter values. Results of the simulations show typical growth phases: a period of fast growth which leads to a period of slower growth where environmental factors are limiting growth. The framework allows for quantitative analysis of the tumor progression, equilibrium and parameter sensitivity. The proposed model is a flexible mathematical framework for the understanding of the dynamics of a tumor and the computational evaluation of therapeutic strategies.
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References
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