On conditions for asymptotic stability in models of pathological entities growth based on the Richard’s dynamic


  • V. P. Martsenyuk
  • O. A. Bagrij-Zayats


The model of common pathological formation development on the basis of Richard’s dynamic is considered. A mathematical model of pathological formation growth process taking into account the immune response is built. The first equation describes the change of cell number of pathological formation in human body. The second equation describes plasma cells growth. The third equation describes the change of number of antibodies that react with receptor cells of pathological formation. The fourth equation describes the extent of organ damage. Structural conditions of asymptotic stability for the model of general pathological formation growth based on Richard dynamic is built. The conditions of local asymptotic stability of the stationary state corresponding to the absence of disease is investigated. Sufficient conditions for asymptotic stability of equilibrium models of pathological formation in terms of the coefficients of the characteristic quazipolynomian is obtained. The numerical analysis of the developed model is carried out, and the resulting math results for specific parameters of the model of the pathological entity are analyzed.


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Methods of system analysis and control in conditions of risk and uncertainty