Mathematical Models of Tumor Growth: From Population Dynamics to Hybrid Models
Year: 2026
Type: conference-paper
Abstract: Tumor progression is governed by mechanisms that span multiple biological scales, from population-level growth to rare cell-level events such as mutation, phenotypic switching, dormancy, and reactivation. As a result, tumor modeling has developed along three main directions: deterministic, stochastic, and hybrid approaches. Deterministic models, most commonly formulated as ordinary differential equations, provide an efficient and accurate description of tumor dynamics and treatment response at large population sizes. However, they are not well suited to capturing rare events and low-cell-number behavior, which are often critical for understanding remission, relapse, and the emergence of resistance. In contrast, stochastic models can represent these phenomena more realistically, but they become computationally expensive at clinically relevant tumor scales. This paper presents a comprehensive review of deterministic and stochastic tumor modeling methods and examines their advantages and limitations and particular emphasis is placed on hybrid strategies. Hybrid models offer a practical balance, making them a promising framework for clinically relevant tumor modeling and therapy design.
Institution: Obuda University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7204188640