Optimal Perturbations of Systems with Delayed Argument for Control of Dynamics of Infectious Diseases Based on Multicomponent Actions

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Abstract

In this paper, we apply optimal perturbations to control mathematical models of infectious diseases expressed as systems of nonlinear differential equations with delayed argument. We develop the method for calculation of perturbations of the initial state of a dynamical system with delayed argument producing maximal amplification in the given local norm taking into account weights of perturbation components. For the model of experimental virus infection, we construct optimal perturbation for two types of stationary states, with low or high virus load, corresponding to different variants of chronic virus infection flow.

About the authors

G A Bocharov

Institute of Numerical Mathematics of the Russian Academy of Sciences; RUDN University

Email: gbocharov@gmail.com
8 Gubkina st., 119333 Moscow, Russia; 6 Miklukho-Maklaya st., 117198 Moscow, Russia

Yu M Nechepurenko

Institute of Numerical Mathematics of the Russian Academy of Sciences; Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences

Email: yumnech@yandex.ru
8 Gubkina st., 119333 Moscow, Russia; 4 Miusskaya sq., 125047 Moscow, Russia

M Yu Khristichenko

Institute of Numerical Mathematics of the Russian Academy of Sciences; Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences

Email: micha.hrist@rambler.ru
8 Gubkina st., 119333 Moscow, Russia; 4 Miusskaya sq., 125047 Moscow, Russia

D S Grebennikov

Institute of Numerical Mathematics of the Russian Academy of Sciences; Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences

Email: dmitry.ew@gmail.com
8 Gubkina st., 119333 Moscow, Russia; 4 Miusskaya sq., 125047 Moscow, Russia

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