Bifurcation Analysis and Optimal Control of a Discrete-Time Tumor Model

Speaker(s)

Anupam Priyadarshi

Affiliation

Banaras Hindu University, India

Language of the talk

English

Date

Oct. 23, 2024, 2:15 p.m.

Room

room 5070

Information about the event

Seminarium odbędzie się online

Seminar

Seminar of Biomathematics and Game Theory Group

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Among several treatment approaches for cancer, immunotherapy has emerged as a highly promising approach in modern cancer treatment. We propose a discretized version of a three-dimensional cancer model to explore the interactions between tumor cells, host cells, and immune cells, highlighting the role of immune cells in reducing tumor cell growth within the tumor-immune interaction dynamics. We investigate the local stability analysis of the system and establish conditions for the existence and stability of the fixed points. The analysis of several bifurcation scenarios, such as flip bifurcation and Neimark- Sacker bifurcation are discussed and conditions in terms of key parameters are established. The extensive numerical simulations are carried out to validate these theoretical results of flip and Neimark–Sacker bifurcations. The system exhibits a rich dynamics including stability, limit cycles, chaos, etc., indicating the coexistence of normal and tumor cells, which exacerbates disease progression. Additionally, the model demonstrates that increasing immune cell levels through immunotherapy can stabilize the chaotic behavior of the tumor population. In cases of uncontrolled tumor growth, we design an optimal control strategy to effectively suppress tumor development. These results offer valuable strategies for managing tumor growth and improving therapeutic interventions.

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