Numerical steady state analysis of the Marchuk–Petrov model of antiviral immune response

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.