Work

Bifurcation mechanism, speed feedback controller, and hybrid controller design in a delayed tumor-immune competitive model

Year: 2025

Type: article

Abstract: In this study, we formulate a delayed tumor-immune competitive model by incorporating dual time delays into the biological interactions, extending prior modeling frameworks. By employing fixed point theory, inequality techniques, and construction of functions, we explore the well-posedness of solutions, including the existence and uniqueness, non-negativity, and boundedness. The new stability and Hopf bifurcation conditions of the proposed model are analytically derived via the Routh–Hurwitz criterion and the bifurcation theory of delayed differential systems. We design two control strategies (namely, a hybrid controller with a state feedback and parameter perturbation with delay and a speed feedback controller) to control the stability domain and bifurcation behavior of the formulated model. These controllers effectively delay or advance bifurcation onset and expand or narrow the system’s stability domain. Numerical simulations validate the analytical findings, illustrating how dual delays influence the stability of equilibrium and bifurcation patterns. The results gained from this article can provide theoretical support for optimizing cancer treatment, emphasizing the critical role of time delays in the tumor immune dynamics.

Source: AIP Advances

DOI: 10.1063/5.0292455

Authors: Qinwen Deng, Changjin Xu, Jinting Lin, Yingyan Zhao

Institution: Guizhou University of Finance and Economics

Language: English

Topic: Mathematical Biology Tumor Growth

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,350

Funder: National Natural Science Foundation of China