Effects of delayed immune-activation in the dynamics of tumor-immune interactions

Parthasakha Das ¹   ; Pritha Das ¹   ; Samhita Das ¹

¹ Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur Howrah, West Bengal, India.

Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 45

Résumé

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.

Détail

DOI : 10.1051/mmnp/2020001

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