Optimal Disturbances of Stationary and Periodic Solutions to Delay Systems in Mathematical Immunology

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Abstract

This work is devoted to optimal disturbances of stationary and periodic solutions to systems of delay differential equations, their computation, and use in mathematical immunology. Original methods for computing the stationary and periodic solutions themselves and tracing them along the system parameters, as well as methods for computing optimal disturbances for these solutions are briefly described. The performance of the described methods is demonstrated using the example of the well-known Marchuk–Petrov model of the antiviral immune response with parameter values corresponding to the infection caused by hepatitis B viruses.

About the authors

Yu. M Nechepurenko

Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences

Email: yumnech@yandex.ru
Moscow, Russia

M. Yu Khristichenko

Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences; NRC Kurchatov Institute

Moscow, Russia

G. A Bocharov

Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences; Sechenov FMSMU

Moscow, Russia

D. S Grebennikov

Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences; Sechenov FMSMU

Moscow, Russia

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