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On the dynamics of a delayed tumor-immune model

S. Asserda, A. Bernoussi, M. El Fatini, A. Kaddar, A. Laaribi

Abstract


In our Knowledge, this is the first attempt to deal with a tumor-immune model with two delays. Our proposed model takes into account the time needed for the immune system to develop a suitable response to the growth of tumor cells, and the time needed for the penetration of tumor cells (TCs) by effector cells (ECs) and the detachment of ECs from TCs. This work is under development, we present here just the basic idea and a qualitative analysis of the model with one delay. For that, we investigate the local stability, the Hopf bifurcation and we give some numerical results. Concerning the competition with two time delays, we mention lastly that we can choose one of the delays as a bifurcation parameter.

Keywords


Tumor, immune system, delay differential equation, stability, Hopf bifurcation.

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