Abstract
A concept of optimal disturbances of periodic solutions for a system of time-delay differential equations is defined. An algorithm for computing the optimal disturbances is proposed and justified. This algorithm is tested on the known system of four nonlinear time-delay differential equations modelling the dynamics of the experimental infection caused by the lymphocytic choriomeningitis virus. The results of numerical experiments are discussed.
Funding statement: The research was supported by the Moscow Center of Fundamental and Applied Mathematics (Agreement 075-15-2019-1624 with the Ministry of Education and Science of the Russian Federation).
References
[1] G. A. Bocharov, Modelling the dynamics of LCMV infection in mice: conventional and exhaustive CTL responses. J. Theor. Biol. 192 (1998), No. 3, 283–308.10.1006/jtbi.1997.0612Search in Google Scholar PubMed
[2] G. A. Bocharov, Yu. M. Nechepurenko, M. Yu. Khristichenko and D. S. Grebennikov, Maximum response perturbation-based control of virus infection model with time-delays. Russ. J. Numer. Anal. Math. Modelling 32 (2017), No. 5, 275–291.10.1515/rnam-2017-0027Search in Google Scholar
[3] G. A. Bocharov, Yu. M. Nechepurenko, M. Yu. Khristichenko and D. S. Grebennikov, Optimal disturbances of bistable time-delay systems modeling virus infections. Doklady Mathematics 98 (2018), No. 1, 313–316.10.1134/S1064562418050058Search in Google Scholar
[4] G. A. Bocharov, Yu. M. Nechepurenko, M. Yu. Khristichenko and D. S. Grebennikov, Optimal perturbations of systems with delayed independent variables for control of dynamics of infectious diseases based on multicomponent actions. J. Math. Sci. 253 (2021), 618–641.10.1007/s10958-021-05258-wSearch in Google Scholar
[5] G. H. Golub and C. F. Van Loan, Matrix Computations. John Hopkins University Press, London, 1989.Search in Google Scholar
[6] E. Hairer and G. Wanner, Solving Ordinary Differential Equations. Springer-Verlag, Berlin, 1996.10.1007/978-3-642-05221-7Search in Google Scholar
[7] J. K. Hale, Theory of Functional Differential Equations. Springer-Verlag, New York, 1977.10.1007/978-1-4612-9892-2Search in Google Scholar
[8] M. Yu. Khristichenko and Yu. M. Nechepurenko, Computation of periodic solutions to models of infectious disease dynamics and immune response. Russ. J. Numer. Anal. Math. Modelling 36 (2021), No. 2, 87–99.10.1515/rnam-2021-0008Search in Google Scholar
[9] G. I. Marchuk, Mathematical Models in Immunology. Optimization Software Inc. Publications Division, New York, 1983.Search in Google Scholar
[10] Yu. M. Nechepurenko and M. Yu. Khristichenko, Computation of optimal disturbances for delay systems. Comput. Maths. Math. Phys. 59 (2019), No. 5, 731–746.10.1134/S0965542519050129Search in Google Scholar
[11] Yu. M. Nechepurenko, M. Yu. Khristichenko, D. S. Grebennikov, and G. A. Bocharov, Bistability analysis of virus infection models with time delays. Discrete and Continuous Dynamical Systems Series S 13 (2020), No. 9, 2385–2401.10.3934/dcdss.2020166Search in Google Scholar
[12] G. W. Stewart, Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices. Numer. Math. 25 (1976), No. 2, 123–126.10.1007/BF01462265Search in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Glacier parameterization in SLAV numerical weather prediction model
- Optimal disturbances for periodic solutions of time-delay differential equations
- Construction and optimization of numerically-statistical projection algorithms for solving integral equations
- Linear regularized finite difference scheme for the quasilinear subdiffusion equation
- On the efficiency of using correlative randomized algorithms for solving problems of gamma radiation transfer in stochastic medium
- Error identities for the reaction–convection–diffusion problem and applications to a posteriori error control
Articles in the same Issue
- Frontmatter
- Glacier parameterization in SLAV numerical weather prediction model
- Optimal disturbances for periodic solutions of time-delay differential equations
- Construction and optimization of numerically-statistical projection algorithms for solving integral equations
- Linear regularized finite difference scheme for the quasilinear subdiffusion equation
- On the efficiency of using correlative randomized algorithms for solving problems of gamma radiation transfer in stochastic medium
- Error identities for the reaction–convection–diffusion problem and applications to a posteriori error control