December  2016, 21(10): 3315-3330. doi: 10.3934/dcdsb.2016099

Minimizing $\mathcal R_0$ for in-host virus model with periodic combination antiviral therapy

1. 

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, United States

2. 

Department of Mathematics, University of Florida, 1400 Stadium Road, Gainesville, FL 32611

Received  December 2015 Revised  May 2016 Published  November 2016

The aim of this article is to provide formulas and properties of the basic reproduction number, $\mathcal R_0$, for a within-host virus model with periodic combination drug treatment. In particular, we extend and further results about how the phase difference between drug treatment can critically affect the asymptotic dynamics of model and corresponding $\mathcal R_0$. Our main theorem establishes that $\mathcal R_0$ is minimized for out-of-phase efficacies and maximized for in-phase efficacies in a special case where drug efficacies are ``bang-bang'' functions.
Citation: Cameron J. Browne, Sergei S. Pilyugin. Minimizing $\mathcal R_0$ for in-host virus model with periodic combination antiviral therapy. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3315-3330. doi: 10.3934/dcdsb.2016099
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show all references

References:
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Mathematical Biosciences and Engineering, 1 (2004), 223-241. doi: 10.3934/mbe.2004.1.223.  Google Scholar

[2]

Journal of Mathematical Biology, 53 (2006), 421-436. doi: 10.1007/s00285-006-0015-0.  Google Scholar

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Mathematical Biosciences, 210 (2007), 647-658. doi: 10.1016/j.mbs.2007.07.005.  Google Scholar

[4]

Journal of Mathematical Biology, 65 (2012), 601-621. doi: 10.1007/s00285-011-0479-4.  Google Scholar

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PhD thesis, University of Florida, 2012. Google Scholar

[6]

Bulletin of Mathematical Biology, 74 (2012), 562-589. doi: 10.1007/s11538-011-9677-x.  Google Scholar

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Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1999-2017. doi: 10.3934/dcdsb.2013.18.1999.  Google Scholar

[8]

Journal of Mathematical Biology, 71 (2015), 215-253. doi: 10.1007/s00285-014-0810-y.  Google Scholar

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Proceedings of the National Academy of Sciences, 112 (2015), 5467-5472. doi: 10.1073/pnas.1419162112.  Google Scholar

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M. A. Nowak and R. M. May, Virus Dynamics,, 2000., ().   Google Scholar

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Bulletin of Mathematical Biology, 69 (2007), 2027-2060. doi: 10.1007/s11538-007-9203-3.  Google Scholar

[17]

Nature Medicine, 18 (2012), 1378-1385. doi: 10.1038/nm.2892.  Google Scholar

[18]

SIAM Journal on Applied Mathematics, 63 (2003), 1313-1327. doi: 10.1137/S0036139902406905.  Google Scholar

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Journal of Dynamics and Differential Equations, 20 (2008), 699-717. doi: 10.1007/s10884-008-9111-8.  Google Scholar

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[22]

Bulletin of Mathematical Biology, 75 (2013), 543-563. doi: 10.1007/s11538-013-9820-y.  Google Scholar

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