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Combination therapy of pegylated interferon and lamivudine and optimal controls for chronic hepatitis B infection

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Abstract

A model for combination therapy of pegylated interferon and lamivudine is presented in this paper. A critical drug efficacy in terms of the parameters of the model comprising of coupled ordinary differential equations is obtained. The dynamics of viral load is greatly impacted by the relation of the efficacies of the individual drugs vis-a-vis the critical efficacy. A control problem is formulated and solved numerically to obtain the optimal therapeutic regimen keeping in mind both biomedical goals and cost constraints.

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References

  1. Ciupe SM, Ribeiro RM, Nelson PW, Perelson AS (2007) Modeling the mechanisms of acute hepatitis B virus infection. J Theor Biol 247(1):23–35

    Article  MathSciNet  Google Scholar 

  2. Lewin S, Walters T, Locarnini S (2002) Hepatitis B treatment: rational combination chemotherapy based on viral kinetic and animal model studies. Antivir Res 55(3):381–396

    Article  Google Scholar 

  3. Thimme R, Wieland S, Steiger C, Ghrayeb J, Reimann KA, Purcell RH, Chisari FV (2003) CD8+ T cells mediate viral clearance and disease pathogenesis during acute hepatitis B virus infection. J Virol 77(1):68–76

    Article  Google Scholar 

  4. Ribeiro RM, Lo A, Perelson AS (2002) Dynamics of hepatitis B virus infection. Microbes Infect 4(8):829–835

    Article  Google Scholar 

  5. Dahari H, Shudo E, Ribeiro RM, Perelson AS (2009) Modeling complex decay profiles of hepatitis B virus during antiviral therapy. Hepatology 49(1):32–38

    Article  Google Scholar 

  6. Murray JM, Purcell RH, Wieland SF (2006) The half-life of hepatitis B virions. Hepatology 44(5):1117–1121

    Article  Google Scholar 

  7. Asselah T, Lada O, Moucari R, Martinot M, Boyer N, Marcellin P (2007) Interferon therapy for chronic hepatitis B. Clin Liver Dis 11(4):839–849

    Article  Google Scholar 

  8. Schalm SW, Heathcote J, Cianciara J, Farrell G, Sherman M, Willems B, Dhillon A, Moorat A, Barber J, Gray DF (2000) Lamivudine and alpha interferon combination treatment of patients with chronic hepatitis B infection: a randomised trial. Gut 46(4):562–568

    Article  Google Scholar 

  9. Severini A, Liu XY, Wilson JS, Tyrrell DL (1995) Mechanism of inhibition of duck hepatitis B virus polymerase by (-)-beta-L-\(2^{\prime },3^{\prime }\)-dideoxy-\(3^{\prime }\)-thiacytidine. Antimicrob Agents Chemother 39(7):1430–1435

    Article  Google Scholar 

  10. Zoulim F (2004) Mechanism of viral persistence and resistance to nucleoside and nucleotide analogs in chronic hepatitis B virus infection. Antivir Res 64(1):1–15

    Article  Google Scholar 

  11. Lewin SR, Ribeiro RM, Walters T, Lau GK, Bowden S, Locarnini S, Perelson AS (2001) Analysis of hepatitis B viral load decline under potent therapy: complex decay profiles observed. Hepatology 34(5):1012–1020

    Article  Google Scholar 

  12. Dahari H, Lo A, Ribeiro RM, Perelson AS (2007) Modeling hepatitis C virus dynamics: liver regeneration and critical drug efficacy. J Theor Biol 247(2):371–381

    Article  MathSciNet  Google Scholar 

  13. Neumann AU, Lam NP, Dahari H, Gretch DR, Wiley TE, Layden TJ, Perelson AS (1998) Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science 282:103–107

    Article  Google Scholar 

  14. Lenhart S, Workman JT (2007) Optimal control applied to biological models. Chapman and Hall/CRC, London

    MATH  Google Scholar 

  15. Swan GW (1990) Role of optimal control theory in cancer chemotherapy. Math Biosci 101(2):237–284

    Article  MATH  Google Scholar 

  16. Murray JM (1990) Some optimal control problems in cancer chemotherapy with a toxicity limit. Math Biosci 100(1):49–67

    Article  MathSciNet  MATH  Google Scholar 

  17. Murray JM (1990) Optimal control for a cancer chemotherapy problem with general growth and loss functions. Math Biosci 98(2):273–287

    Article  MathSciNet  MATH  Google Scholar 

  18. de Pillis LG, Gu W, Fister KR, Head T, Maples K, Murugan A, Neal T, Yoshida K (2007) Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls. Math Biosci 209(1):292–315

    Article  MathSciNet  MATH  Google Scholar 

  19. Fister KR, Panetta JC (2003) Optimal control applied to competing chemotherapeutic cell-kill strategies. SIAM J Appl Math 63(6):1954–1971

    Article  MathSciNet  MATH  Google Scholar 

  20. Chavez IYS, Morales-Menendez R, Chapa SOM (2009) Glucose optimal control system in diabetes treatment. Appl Math Comput 209(1):19–30

    MathSciNet  MATH  Google Scholar 

  21. Nanda S, Moore H, Lenhart S (2007) Optimal control of treatment in a mathematical model of chronic myelogenous leukemia. Math Biosci 210(1):143–156

    Article  MathSciNet  MATH  Google Scholar 

  22. Kirschner D, Lenhart S, Serbin S (1997) Optimal control of the chemotherapy of HIV. J Math Biol 35(7):775–792

    Article  MathSciNet  MATH  Google Scholar 

  23. Joshi HR (2002) Optimal control of an HIV immunology model. Optim Control Appl Methods 23(4):199–213

    Article  MathSciNet  MATH  Google Scholar 

  24. Adams BM, Banks HT, Davidian M, Kwon H-D, Tran HT, Wynne SN, Rosenberg ES (2005) HIV dynamics: modeling, data analysis, and optimal treatment protocols. J Comput Appl Math 184(1):10–49

    Article  MathSciNet  MATH  Google Scholar 

  25. Stengel RF (2008) Mutation and control of the human immunodeficiency virus. Math Biosci 213(2):93–102

    Article  MathSciNet  MATH  Google Scholar 

  26. Chakrabarty SP, Joshi HR (2009) Optimally controlled treatment strategy using interferon and ribavirin for hepatitis C. J Biol Syst 17(1):97–110

    Article  MathSciNet  MATH  Google Scholar 

  27. Chakrabarty SP (2009) Optimal efficacy of ribavirin in the treatment of hepatitis C. Optim Control Appl Methods 30(6):594–600

    Article  MathSciNet  Google Scholar 

  28. Pachpute G, Chakrabarty SP (2013) Dynamics of hepatitis C under optimal therapy and sampling based analysis. Commun Nonlinear Sci Numer Simul 18(8):2202–2212

    Article  MathSciNet  MATH  Google Scholar 

  29. Martin NK, Pitcher AB, Vickerman P, Vassall A, Hickman M (2011) Optimal control of hepatitis C antiviral treatment programme delivery for prevention amongst a population of injecting drug users. PLoS ONE 6(8):e22309

    Article  Google Scholar 

  30. Manna K, Chakrabarty SP (2015) Chronic hepatitis B infection and HBV DNA-containing capsids: modeling and analysis. Commun Nonlinear Sci Numer Simul 22(1–3):383–395

    Article  MathSciNet  MATH  Google Scholar 

  31. Srivastava PK, Chandra P (2010) Modeling the dynamics of HIV and CD4+ T cells during primary infection. Nonlinear Anal Real World Appl 11(2):612–618

    Article  MathSciNet  MATH  Google Scholar 

  32. van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180(1–2):29–48

    Article  MathSciNet  MATH  Google Scholar 

  33. Heffernan JM, Smith RJ, Wahl LM (2005) Perspectives on the basic reproductive ratio. J R Soc Interface 2(4):281–293

    Article  Google Scholar 

  34. Adams BM, Banks HT, Kwon H-D, Tran HT (2004) Dynamic multidrug therapies for HIV: optimal and STI control approaches. Math Biosci Eng 1(2):223–241

    Article  MathSciNet  MATH  Google Scholar 

  35. Fister KR, Lenhart S, McNally JS (1998) Optimizing chemotherapy in an HIV model. Electron J Differ Equ 32:1–12

    MathSciNet  MATH  Google Scholar 

  36. Fleming WH, Rishel RW (1975) Deterministic and stochastic optimal control. Springer, Berlin

    Book  MATH  Google Scholar 

  37. Garira W, Musekwa SD, Shiri T (2005) Optimal control of combined therapy in a single strain HIV-1 model. Electron J Differ Equ 52:1–22

    MathSciNet  MATH  Google Scholar 

  38. Chakrabarty SP, Banerjee S (2010) A control theory approach to cancer remission aided by an optimal therapy. J Biol Syst 18(1):75–91

    Article  MathSciNet  MATH  Google Scholar 

  39. Burden T, Ernstberger J, Fister KR (2004) Optimal control applied to immunotherapy. Discrete Cont Dyn Syst Ser B 4(1):135–146

    MathSciNet  MATH  Google Scholar 

  40. Kirk DE (2004) Optimal control theory: an introduction. Dover Publications, Mineola

    Google Scholar 

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Acknowledgements

The first author gratefully acknowledges the financial support provided by the Indian Institute of Technology Guwahati for pursuing his Ph.D. The authors express their gratitude to the reviewers for their comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Kalyan Manna & Siddhartha P. Chakrabarty

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  1. Kalyan Manna
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  2. Siddhartha P. Chakrabarty
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Correspondence to Siddhartha P. Chakrabarty.

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Manna, K., Chakrabarty, S.P. Combination therapy of pegylated interferon and lamivudine and optimal controls for chronic hepatitis B infection. Int. J. Dynam. Control 6, 354–368 (2018). https://doi.org/10.1007/s40435-017-0306-x

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  • DOI: https://doi.org/10.1007/s40435-017-0306-x

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