The impact of infected T lymphocyte burst rate and viral shedding rate on optimal treatment scheduling in a human immunodeficiency virus infection

Authors

  • Anuraag Bukkuri University of Minnesota

DOI:

https://doi.org/10.11145/j.biomath.2020.08.173

Keywords:

Optimal Control, HIV, Reverse Transcriptase Inhibitors, Protease Inhibitors

Abstract

We consider a mathematical model of human immunodeficiency virus (HIV) infection dynamics of T lymphocyte (T cell), infected T cell, and viral populations under reverse transcriptase inhibitor (RTI) andprotease inhibitor (PI) treatment. Existence, uniqueness, and characterization of optimal treatment profiles which minimize total amount of drug used, viral, and infected T cell populations, while maximizing levels of T cells are determined analytically. Numerical optimal control experiments are also performed to illustrate how burst rate of infected T cells and shedding rate of virions impact optimal treatment profiles. Finally, a sensitivity analysis is performed to detect how model input parameters contribute to output variance.

References

Arts AJ, Hazuda DK (2012). HIV-1 Antiretroviral Drug Therapy. textit{Cold Spring Harbor Prespectives in Medicine} 2, 1-23. newline

Autran B, Carcelain G, Li TS, Blanc C, Mathez D, Tubiana R, Katlama C, Debre P, Leibowitch J (1997). Positive effects of combined antiretroviral therapy on CD4+ T cell homeostasis and function in advanced HIV disease. textit{Science} 277, 112 –116. newline

Bracq L, Xie M, Benichou S, Bouchet J (2018). Mechanisms for Cell-to-Cell Transmission of HIV-1. textit{Front. in Immuno.} 9:260, 1-14. newline

Bukkuri A (2019). Optimal control analysis of combined anti-angiogenic and tumor immunotherapy. textit{Open Jour. of Math. Sci.} 3, 349-357. newline

Burden T, Ernstberger J, Fister R (2004). Optimal Control Applied to Immunotherapy. textit{Discrete and Continuous Dynamical Systems} 4(1), 135–146.newline

Chen HY, Mascio MD, Perelson AS, Ho DD, Zhang L (2007). Determination of virus burst size in vivo using a single-cycle SIV in rhesus macaques. textit{PNAS} 104(48), 19079-19084. newline

Cunningham AL, Donaghy H, Harman AN, Kim M, Turville SG (2010). Manipulation of dendritic cell function by viruses. textit{Curr. Op. in Microbiol.} 13 (4), 524–529. newline

Deininger MWN, Druker BJ (2003). Specific targeted therapy of chronic myelogenous leukemia with imatinib. textit{Pharmacol. Rev.} 55(3), 401-423. newline

Duda Z (1997). Numerical solutions to bilinear models arising in cancer chemotherapy. textit{Nonlinear World} 4, 53-72. newline

Fister R, Lenhart S, McNally J (1998). Optimizing Chemotherapy in an HIV , Elec. J.DE., 32, 1–12. newline

Fleming W, Rishel R (1975). Deterministic and Stochastic Optimal Control. textit{Springer-Verlag}. newline

Gotte M, Wainberg MA (2000). Biochemical mechanisms involved in overcoming HIV resistance to nucleoside inhibitors of reverse transcriptase. textit{Drug Resist. Update} 3, 30 –38. newline

Gulnik SV, Suvorov LI, Liu B, Yu B, Anderson B, Mitsuya H, Erickson JW (1995). Kinetic characterization and cross-resistance patterns of HIV-1 protease mutants selected under drug pressure. textit{Biochem.} 34, 9282–9287.newline

Hyman P, Abedon ST (2009). Practical methods for determining phage growth parameters. textit{Methods Mol. Biol.} 501, 175-202. newline

Jung E, Lenhart S, Feng Z (2002). Optimal control of treatments in a two-strain tuberculosis model. textit{Discrete Contin.Dyn. Syst. Ser.} 2, 473-482. newline

Komanduri KV, Viswanathan MN, Wieder ED, Schmidt DK, Bredt BM, Jacobson MA, McCune JM (1998). Restoration of cytomegalovirus-specific CD4+ T-lymphocyte responses after ganciclovir and highly active antiretroviral therapy in individuals infected with HIV-1. textit{Nat. Med.} 4, 953–956. newline

Layne SP, Spouge JL, Dembo M (1989). Quantifying the infectivity of HIV. textit{Proc. Natl. Acad. Sci. U.S.A.} 86, 4644-4648. newline

Lederman MM, Connick E, Landay A, Kuritzkes DR, Spritzler J, St Clair M, Kotzin BL, Fox L, Chiozzi MH, Leonard JM, et al. (1998). Immunologic responses associated with 12 weeks of combination antiretroviral therapy consisting of zidovudine, lamivudine, and ritonavir: Results of AIDS Clinical Trials Group Protocol 315. textit{J. Infect. Dis.} 178, 70–79. newline

Lukes D (1982). Differential Equations: Classical to Controlled. textit{Math. in Sci. and Engrg.} 162. newline

Michaud V, Bar-Magen T, Turgeon J, Flockhart D, Desta Z, Wainberg MA (2012). The dual role of pharmacogenetics in HIV treatment: mutations and polymorphisms regulating antiretroviral drug resistance and disposition. textit{Pharmacol. Rev.} 64(3), 803-833. newline

Mobisa B, Lawi GO, Nthiiri JK (2018). Modelling In Vivo HIV Dynamics under Combined Antiretroviral Treatment. textit{Jour. App. Math.} (2018), 1-11. newline

PENTA (2004). Highly active antiretroviral therapy started in infants under 3 months of age: 72-week follow-up for CD4 cell count, viral load and drug resistance outcome. textit{AIDS} 18(2), 237-245. newline

Perelson AS, Kirschner DE, Boer RD (1993). Dynamics of HIV infection of CD4+ T cells. textit{Math. Biosci.} 114(1), 81–125. newline

Tronstein E, Johnston C, Huang M, Selke S, Magaret A, Warren T, Corey L, Wald A (2011). Genital Shedding of Herpes Simplex Virus Among Symptomatic and Asymptomatic Persons With HSV-2 Infection. textit{JAMA} 305(14), 1441-1449. newline

UNAIDS, WHO (2007). 2007 AIDS epidemic update (PDF). p.10. Retrieved January 2, 2020. newline

Zhang XY, Trame MN, Lesko LJ, Schmidt S (2015). Sobol Sensitivity Analysis: A Tool to Guide the Development and Evaluation of Systems Pharmacology Models. textit{CPT Pharmacometrics Syst. Pharmacol.} 4, 69-79. newline

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Published

2020-09-12

Issue

Vol. 9 No. 2 (2020)

Section

Original Articles

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