Abstract
The problem of guaranteed computation of all steady states of the Marchuk–Petrov model with fixed values of parameters and analysis of their stability are considered. It is shown that the system of ten nonlinear equations, nonnegative solutions of which are steady states, can be reduced to a system of two equations. The region of possible nonnegative solutions is analytically localized. An effective technology for computing all nonnegative 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.
Acknowledgment
The authors are grateful to Dmitry S. Grebennikov and Michael Yu. Khristichenko for their help and fruitful discussions.
Funding: The work was supported by the Russian Science Foundation (project No. 17–71–20149) (the development and implementation of numerical methods) and the Russian Science Foundation (project No. 18–11–00171) (the numerical analysis of the Marchuk–Petrov model).
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