Mathematical Analysis of Hepatitis B Virus Combination Treatment

  • Conference paper
  • First Online:
New Trends in the Applications of Differential Equations in Sciences (NTADES 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 412))

  • 364 Accesses

Abstract

In the current paper, we research the influence of IL-2 therapy and we introduce the regulation by distributed feedback control. The results of the stability analysis are presented. We use the Cauchy matrix C(ts), in order to study the behavior (stability) of corresponding system of integro-differential equations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 181.89
Price includes VAT (Germany)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 235.39
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
EUR 235.39
Price includes VAT (Germany)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Tang LSY, Covert E, Wilson E, Kottilil S. Chronic Hepatitis B Infection: A Review. JAMA. 2018 May 1;319(17):1802-1813. https://doi.org/10.1001/jama.2018.3795.Erratum in: JAMA. 2018 Sep 18;320(11):1202. PMID: 29715359.

  2. Parkin DM. The global health burden of infection-associated cancers in the year 2002. Int J Cancer. 2006 Jun 15;118(12):3030-44. https://doi.org/10.1002/ijc.21731.PMID: 16404738.

  3. European Association for the Study of the Liver. Electronic address: easloffice@easloffice.eu; European Association for the Study of the Liver. EASL 2017 Clinical Practice Guidelines on the management of hepatitis B virus infection. J Hepatol. 2017 Aug;67(2):370-398. https://doi.org/10.1016/j.jhep.2017.03.021.Epub 2017 Apr 18. PMID: 28427875.

  4. Tenney DJ, Rose RE, Baldick CJ, Pokornowski KA, Eggers BJ, Fang J, Wichroski MJ, Xu D, Yang J, Wilber RB, Colonno RJ. Long-term monitoring shows hepatitis B virus resistance to entecavir in nucleoside-naïve patients is rare through 5 years of therapy. Hepatology. 2009 May;49(5):1503-14. https://doi.org/10.1002/hep.22841.PMID: 19280622.

  5. Buster EH, Flink HJ, Cakaloglu Y, Simon K, Trojan J, Tabak F, So TM, Feinman SV, Mach T, Akarca US, Schutten M, Tielemans W, van Vuuren AJ, Hansen BE, Janssen HL. Sustained HBeAg and HBsAg loss after long-term follow-up of HBeAg-positive patients treated with peginterferon alpha-2b. Gastroenterology. 2008 Aug;135(2):459-67. https://doi.org/10.1053/j.gastro.2008.05.031.Epub 2008 May 15. PMID: 18585385.

  6. Marcellin P, Lau GK, Bonino F, Farci P, Hadziyannis S, ** R, Lu ZM, Piratvisuth T, Germanidis G, Yurdaydin C, Diago M, Gurel S, Lai MY, Button P, Pluck N; Peginterferon Alfa-2a HBeAg-Negative Chronic Hepatitis B Study Group. Peginterferon alfa-2a alone, lamivudine alone, and the two in combination in patients with HBeAg-negative chronic hepatitis B. N Engl J Med. 2004 Sep 16;351(12):1206-17. https://doi.org/10.1056/NEJMoa040431.PMID: 15371578.

  7. Buti M, Tsai N, Petersen J, Flisiak R, Gurel S, Krastev Z, Aguilar Schall R, Flaherty JF, Martins EB, Charuworn P, Kitrinos KM, Subramanian GM, Gane E, Marcellin P. Seven-year efficacy and safety of treatment with tenofovir disoproxil fumarate for chronic hepatitis B virus infection. Dig Dis Sci. 2015 May;60(5):1457-64. https://doi.org/10.1007/s10620-014-3486-7.Epub 2014 Dec 23. PMID: 25532501; PMCID: PMC4427621.

  8. Monsalve-De Castillo F, Romero TA, Estévez J, Costa LL, Atencio R, Porto L, Callejas D. Concentrations of cytokines, soluble interleukin-2 receptor, and soluble CD30 in sera of patients with hepatitis B virus infection during acute and convalescent phases. Clin Diagn Lab Immunol. 2002 Nov;9(6):1372-5. https://doi.org/10.1128/cdli.9.6.1372-1375.2002.PMID: 12414777; PMCID: PMC130099.

  9. Colombatto P, Civitano L, Bizzarri R, Oliveri F, Choudhury S, Gieschke R, Bonino F, Brunetto MR; Peginterferon Alfa-2a HBeAg-Negative Chronic Hepatitis B Study Group. A multiphase model of the dynamics of HBV infection in HBeAg-negative patients during pegylated interferon-alpha2a, lamivudine and combination therapy. Antivir Ther. 2006;11(2):197-212. PMID: 16640101.

    Google Scholar 

  10. Nowak MA, Bonhoeffer S, Hill AM, Boehme R, Thomas HC, McDade H. Viral dynamics in hepatitis B virus infection. Proc Natl Acad Sci U S A. 1996 Apr 30;93(9):4398-402. https://doi.org/10.1073/pnas.93.9.4398.PMID: 8633078; PMCID: PMC39549.

  11. Perelson AS, Ribeiro RM. Hepatitis B virus kinetics and mathematical modeling. Semin Liver Dis. 2004;24 Suppl 1:11-6. https://doi.org/10.1055/s-2004-828673.PMID: 15192796.

  12. Fatehi Chenar F, Kyrychko YN, Blyuss KB. Mathematical model of immune response to hepatitis B. J Theor Biol. 2018 Jun 14;447:98-110. https://doi.org/10.1016/j.jtbi.2018.03.025.Epub 2018 Mar 21. PMID: 29574141.

  13. A. Domoshnitsky, I.Volinsky, M.Bershadsky, Around the Model of Infection Disease: The Cauchy Matrix and Its Properties, Symmetry 2019, 11(8),1016; https://doi.org/10.3390/sym11081016

  14. Alexander Domoshnitsky, Irina Volinsky and Olga Pinhasov, Some developments in the model of testosterone regulation, AIP Conference Proceedings 2159, 030010, (2019); https://doi.org/10.1063/1.5127475

  15. Yousdi, N.; Hattaf, K.; Rachik, M. Analysis of a HCV model with CTL and antibody responses. Appl. Math. Sci. 3, 2009, 2835–2845.

    MathSciNet  MATH  Google Scholar 

  16. Chenar, F.F.; Kyrychko, Y.N.; Blyuss, K.B. Mathematical model of immune response to hepatitis B. J. Theor. Biol., 2018, 447, 98–110.

    Article  MathSciNet  MATH  Google Scholar 

  17. Domoshnitsky, A.; Volinsky, I.; Polonsky, A.; Sitkin, A. Stabilization by delay distributed feedback control. Math. Model. Nat. Phenom. 2017, 12, 91–105 https://doi.org/10.1051/mmnp/2017067.

    Article  MathSciNet  MATH  Google Scholar 

  18. Domoshnitsky, A.; Volinsky, I.; Polonsky, A. Stabilization of third order differential equation by delay distributed feedback control with unbounded memory. Math. Slovaca 2019, 69, 1165–1176. https://doi.org/10.1515/ms-2017-0298.

    Article  MathSciNet  MATH  Google Scholar 

  19. Domoshnitsky, A.; Volinsky, I.; Bershadsky, M. Around the Model of Infection Disease: The Cauchy Matrix and Its Properties. Symmetry 2019, 11, 1016; https://doi.org/10.3390/sym11081016.

    Article  Google Scholar 

  20. Bershadsky, M.; Chirkov, M.; Domoshnitsky, A.; Rusakov, S.; Volinsky, I. Distributed Control and the Lyapunov Characteristic Exponents in the Model of Infectious Diseases. Complexity 2019, 2019, 5234854, https://doi.org/10.1155/2019/5234854.

    Article  MATH  Google Scholar 

  21. Domoshnitsky, A.; Volinsky, I.; Levi, S.; Shemesh, S. Stability of third order neutral delay differential equations. AIP Conf. Proc. 2019, 2159, 020002, https://doi.org/10.1063/1.5127464.

    Article  Google Scholar 

  22. Domoshnitsky, A.; olinsky, I.; Pinhasov, O.; Bershadsky, M. Questions of Stability of Functional Differential Systems around the Model of Testosterone Regulation. Bound. Value Probl. 2019, 1, 1–13; https://doi.org/10.1186/s13661-019-01295-2.

  23. Domoshnitsky, A.; Volinsky, I.; Polonsky, A.; Sitkin, A. Practical constructing the Cauchy function of integro-differential equation, Funct. Differ. Equations 2016, 23, 109–118.

    MathSciNet  MATH  Google Scholar 

  24. Volinsky I., Lombardo S.D., Cheredman P. Stability Analysis and Cauchy Matrix of a Mathematical Model of Hepatitis B Virus with Control on Immune System near Neighborhood of Equilibrium Free Point, Symmetry, 13 (2), 166, 2021.

    Article  Google Scholar 

  25. Volinsky I. Stability Analysis of a Mathematical Model of Hepatitis B Virus with Unbounded Memory Control on the Immune System in the Neighborhood of the Equilibrium Free Point, Symmetry, 13 (8), 1437, 2021.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Irina Volinsky .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Volinsky, I. (2023). Mathematical Analysis of Hepatitis B Virus Combination Treatment. In: Slavova, A. (eds) New Trends in the Applications of Differential Equations in Sciences. NTADES 2022. Springer Proceedings in Mathematics & Statistics, vol 412. Springer, Cham. https://doi.org/10.1007/978-3-031-21484-4_22

Download citation

Publish with us

Policies and ethics

Navigation