Stability Analysis of Time Delay Model of Crosstalk between ERK and STAT5a Interaction

In this paper we investigate the qualitative behavior of a time delay model of the crosstalk between ERK and STAT5. We apply linear approximation to study the time delay model. The influence of some parameters on the dynamics of the model is analyzed analytically and numerically. Our qualitative results show that the model is structurally unstable. Relating this result to the physiological nature of the studied mathematical model, we prove mathematically the appearance of a crosstalk between the signaling pathways ERK and STAT in some cancer cells. This pathology appears when the process of homeostasis is disturbed and it has a non-reverse character.

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