The passage from delay equation to ODE system in the model of the tumor markers network

This paper is devoted to a numerical analysis of the solutions of systems of equations describing the dynamics of the concentration of p53 and Mdm2 proteins in their interaction. We consider two interrelated mathematical models of the p53-Mdm2 network. The first model of the proteins concentrations dynamics includes the system of two nonlinear equations with the retarded argument. The second model describes hypothetical stages of process and uses the simplest ODE of higher dimension. We show numerically that in the passage to the limit in which the second model has sufficiently many stages we obtain model based equation with retarded argument. A mathematical model of the network p53-Mdm2-miRNA was constructed. The numerical analysis of the passage to the limit in this mathematical model was carried out.