The mathematical model of the dynamics of the tumor markers network p53-Mdm2-microRNA for microRNA class with a direct positive connection with p53 was formulated. Numerical investigation of the microRNA functioning in conditions of the deregulation of p53 and p53-Mdm2-network was carried out. The deregulation of microRNA in detail was studied. The situations in which p53, its inhibitor Mdm2 and microRNAs exhibit critical properties for the patient's status and can be identified as diagnostic markers of cancer and neurodegenerative disease were studied. The results of numerical analysis are in good agreement with the data of clinical and laboratory studies of known microRNAs.