A dynamic p53-mdm2 model with distributed delay

Specific activator and repressor transcription factors which bind to specific regulator DNA sequences, play an important role in gene activity control. Interactions between genes coding such transcripion factors should explain the different stable or sometimes oscillatory gene activities characteristic for different tissues. In this paper, the dynamic P53-Mdm2 interaction model with distributed delays is investigated. Both weak and Dirac kernels are taken into consideration. For Dirac case, the Hopf bifurcation is investigated. Some numerical examples are finally given for justifying the theoretical results.