| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Cancer modelling
|
|
|---|---|---|
| Article Number | 45 | |
| Number of page(s) | 27 | |
| DOI | https://doi.org/10.1051/mmnp/2020001 | |
| 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,
Shibpur Howrah,
West Bengal, India.
* Corresponding author. parthasakha87das@gmail.com
Received:
11
May
2019
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
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