The problem of guaranteed computation of all steady states of the Marchuk-Petrov model with fixed values of parameters and analysis of their stability is considered. It is shown that the system of ten nonlinear equations, non-negative solutions of which are steady states, can be reduced to a system of two equations. Region of possible non-negative solutions is analytically localized. An effective technology for computing all non-negative solutions and analyzing their stability is proposed. The obtained results provide a computational basis for the study of chronic forms of viral infections using the Marchuk-Petrov model.

viral infection, immune response, Marchuk-Petrov model, delayed equations, steady states, stability

Mathematical modelling in actual problems of science and technics

Sklyarova Ekaterina Vitalievna,  ,  KIAM RAS

Nechepurenko Yuri Mikhailovich,  ,  ИВМ РАН

Bocharov Gennady Alekseevich,  ,  ИВМ РАН