Analytical Study of the Existence of a Hopf Bifurcation in the Tumor Cell Growth with Time Delay


Andi Yusnaeni, - and Kasbawati, - and Syamsuddin Toaha, - Analytical Study of the Existence of a Hopf Bifurcation in the Tumor Cell Growth with Time Delay. Indonesian Journal of Pure and Applied Mathematics, 2021.

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Abstract (Abstrak)

In this paper we study a mathematical model of an immune response system consisting of a number of immune cells that work together to protect the human body from invading tumor cells. The delay differential equation is used to model the immune system caused by a natural delay in the activation process of immune cells. Analytical studies are focused on finding conditions in which the system undergoes changes in stability near a tumor-free steady-state solution. We found that the existence of a tumor-free steady-state solution was warranted when the number of activated effector cells was sufficiently high. By considering the lag of stimulation of helper cell production as the bifurcation parameter, a critical lag is obtained that determines the threshold of the stability change of the tumor- free steady state. It is also leading the system undergoes a Hopf bifurcation to periodic solutions at the tumor-free steady-state solution.

Item Type: Article
Subjects: Q Science > QA Mathematics
Depositing User: - Andi Anna
Date Deposited: 22 Nov 2021 03:00
Last Modified: 22 Nov 2021 03:00
URI: http://repository.unhas.ac.id:443/id/eprint/11328

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