Math. Model. Nat. Phenom.
Volume 15, 2020
|Number of page(s)||27|
|Published online||24 September 2020|
Effects of delayed immune-activation in the dynamics of tumor-immune interactions
Department of Mathematics, Indian Institute of Engineering Science and Technology,
West Bengal, India.
* Corresponding author. email@example.com
Accepted: 26 January 2020
This article presents the impact of distributed and discrete delays that emerge in the formulation of a mathematical model of the human immunological system describing the interactions of effector cells (ECs), tumor cells (TCs) and helper T-cells (HTCs). We investigate the stability of equilibria and the commencement of sustained oscillations after Hopf-bifurcation. Moreover, based on the center manifold theorem and normal form theory, the expression for direction and stability of Hopf-bifurcation occurring at tumor presence equilibrium point of the system has been derived explicitly. The effect of distributed delay involved in immune-activation on the system dynamics of the tumor is demonstrated. Numerical simulations are also illustrated for elucidating the change of dynamic behavior by varying system parameters.
Mathematics Subject Classification: 97M60 / 37C75 / 65P30
Key words: Tumor-immune system interactions / delay differential equations / immune-activation distributed delay / Hopf-bifurcation
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.