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Dependence of optimal disturbances on periodic solution phases for time-delay systems

  • Michael Yu. Khristichenko EMAIL logo , Yuri M. Nechepurenko and Gennady A. Bocharov
Published/Copyright: April 11, 2023

Abstract

The paper is focused on the dependence of optimal disturbances of stable periodic solutions of time-delay systems on phases of such solutions. The results of numerical experiments with the well-known model of the dynamics of infection caused by lymphocytic choriomeningitis virus are presented and discussed. A new more efficient method for computing the optimal disturbances of periodic solutions is proposed and used.

MSC 2010: 92B05; 92C42; 93C23; 93B35; 93C73; 92-08

Funding statement: The research was supported by the Moscow Center of Fundamental and Applied Mathematics at INM RAS (Agreement with the Ministry of Education and Science of the Russian Federation No. 075-15-2022-286).

References

[1] S. Bernard, B. Cajavec Bernard, F. Levi, and H. Herzel, Tumor growth rate determines the timing of optimal chronomodulated treatment schedules. PLoS Comput. Biol. 6 (2010), No. 3, e1000712.10.1371/journal.pcbi.1000712Search in Google Scholar PubMed PubMed Central

[2] 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

[3] 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

[4] G. A. Bocharov, Yu. M. Nechepurenko, M. Yu. Khristichenko, and D. S. Grebennikov, Optimal disturbances of bistable time-delay systems modelling virus infections. Doklady Math. 98 (2018), No. 1, 313–316.10.1134/S1064562418050058Search in Google Scholar

[5] 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

[6] B. F. Dibrov, Resonance effect in self-renewing tissues. J. Theor. Biol. 192 (1998), No. 1, 15–33.10.1006/jtbi.1997.0613Search in Google Scholar PubMed

[7] G. C. Fanning, F. Zoulim, J. Hou, and A. Bertoletti, Therapeutic strategies for hepatitis B virus infection: towards a cure. Nat. Rev. Drug Discov. 18 (2019), No. 11, 827–844.10.1038/s41573-019-0037-0Search in Google Scholar PubMed

[8] F. Fatehi, R. J. Bingham, Stockley P. G., and R. Twarock, An age-structured model of hepatitis B viral infection highlights the potential of different therapeutic strategies. Sci. Rep. 12 (2022), No. 1, 1–12.10.1038/s41598-021-04022-zSearch in Google Scholar PubMed PubMed Central

[9] A. Gillis, M. Beil, K. Halevi-Tobias, P. V. van Heerden, S. Sviri, and Z. Agur, Alleviation of exhaustion-induced immunosuppression and sepsis by immune checkpoint blockers sequentially administered with antibiotics-analysis of a new mathematical model. Intensive Care Med. Exp. 7 (2019), No. 1, 1–16.10.1186/s40635-019-0260-3Search in Google Scholar PubMed PubMed Central

[10] G. H. Golub and C. F. Van Loan, Matrix Computations. John Hopkins Univ. Press, 1989.Search in Google Scholar

[11] E. Hairer and G. Wanner, Solving Ordinary Differential Equations. Springer-Verlag, Berlin, 1996.10.1007/978-3-642-05221-7Search in Google Scholar

[12] M. Iannacone and L. G. Guidotti, Immunobiology and pathogenesis of hepatitis B virus infection. Nat. Rev. Immunol. 22 (2022), No. 1, 19–32.10.1038/s41577-021-00549-4Search in Google Scholar PubMed

[13] 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

[14] M. Yu. Khristichenko and Yu. M. Nechepurenko, Optimal disturbances for periodic solutions of time-delay differential equations. Russ. J. Numer. Anal. Math. Modelling 37 (2022), No. 4, 203–212.10.1515/rnam-2022-0017Search in Google Scholar

[15] K. C. K. Lau, K. W. Burak, and C. S. Coffin, Impact of hepatitis B virus genetic variation, integration, and lymphotropism in antiviral treatment and oncogenesis. Microorganisms 8 (2020), No. 10, 1470.10.3390/microorganisms8101470Search in Google Scholar PubMed PubMed Central

[16] 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

[17] 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

[18] B. N. Parlett, The Symmetric Eigenvalue Problem. SIAM, Berkeley, 1998.10.1137/1.9781611971163Search in Google Scholar

[19] W. Yao, L. Hertel, and L. M. Wahl, Dynamics of recurrent viral infection.Proc. Biol. Sci. 273 (2006), No. 1598, 2193–2199.10.1098/rspb.2006.3563Search in Google Scholar PubMed PubMed Central

Received: 2022-11-29
Revised: 2022-12-22
Accepted: 2023-02-01
Published Online: 2023-04-11
Published in Print: 2023-03-28

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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