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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 |
References:
[1] |
B. Adams, H. Banks, H. Kwon and H. Tran, Dynamic multidrug therapies for HIV: Optimal and STI control approaches, Mathematical Biosciences and Engineering, 1 (2004), 223-241.
doi: 10.3934/mbe.2004.1.223. |
[2] |
N. Bacaër and S. Guernaoui, The epidemic threshold of vector-borne diseases with seasonality, Journal of Mathematical Biology, 53 (2006), 421-436.
doi: 10.1007/s00285-006-0015-0. |
[3] |
N. Bacaër and R. Ouifki, Growth rate and basic reproduction number for population models with a simple periodic factor, Mathematical Biosciences, 210 (2007), 647-658.
doi: 10.1016/j.mbs.2007.07.005. |
[4] |
N. Bacaër et al., On the biological interpretation of a definition for the parameter r 0 in periodic population models, Journal of Mathematical Biology, 65 (2012), 601-621.
doi: 10.1007/s00285-011-0479-4. |
[5] |
C. Browne, Two Extensions of a Classical Virus Model, PhD thesis, University of Florida, 2012. |
[6] |
C. J. Browne and S. S. Pilyugin, Periodic multidrug therapy in a within-host virus model, Bulletin of Mathematical Biology, 74 (2012), 562-589.
doi: 10.1007/s11538-011-9677-x. |
[7] |
C. J. Browne and S. S. Pilyugin, Global analysis of age-structured within-host virus model, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1999-2017.
doi: 10.3934/dcdsb.2013.18.1999. |
[8] |
C. J. Browne, R. J. Smith and L. Bourouiba, From regional pulse vaccination to global disease eradication: Insights from a mathematical model of poliomyelitis, Journal of Mathematical Biology, 71 (2015), 215-253.
doi: 10.1007/s00285-014-0810-y. |
[9] |
J. M. Conway and A. S. Perelson, Post-treatment control of HIV infection, Proceedings of the National Academy of Sciences, 112 (2015), 5467-5472.
doi: 10.1073/pnas.1419162112. |
[10] |
P. De Leenheer, Within-host virus models with periodic antiviral therapy, Bulletin of Mathematical Biology, 71 (2009), 189-210.
doi: 10.1007/s11538-008-9359-5. |
[11] |
P. De Leenheer and S. S. Pilyugin, Multistrain virus dynamics with mutations: A global analysis, Mathematical Medicine and Biology, 25 (2008), 285-322.
doi: 10.1093/imammb/dqn023. |
[12] |
N. M. Dixit and A. S. Perelson, Complex patterns of viral load decay under antiretroviral therapy: Influence of pharmacokinetics and intracellular delay, Journal of Theoretical Biology, 226 (2004), 95-109.
doi: 10.1016/j.jtbi.2003.09.002. |
[13] |
A. d'Onofrio, Periodically varying antiviral therapies: Conditions for global stability of the virus free state, Applied Mathematics and Computation, 168 (2005), 945-953.
doi: 10.1016/j.amc.2004.09.014. |
[14] | |
[15] |
A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Review, 41 (1999), 3-44.
doi: 10.1137/S0036144598335107. |
[16] |
L. Rong, Z. Feng and A. S. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment, Bulletin of Mathematical Biology, 69 (2007), 2027-2060.
doi: 10.1007/s11538-007-9203-3. |
[17] |
D. I. Rosenbloom, A. L. Hill, S. A. Rabi, R. F. Siliciano and M. A. Nowak, Antiretroviral dynamics determines hiv evolution and predicts therapy outcome, Nature Medicine, 18 (2012), 1378-1385.
doi: 10.1038/nm.2892. |
[18] |
H. L. Smith and P. De Leenheer, Virus dynamics: a global analysis, SIAM Journal on Applied Mathematics, 63 (2003), 1313-1327.
doi: 10.1137/S0036139902406905. |
[19] |
W. Wang and X.-Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, Journal of Dynamics and Differential Equations, 20 (2008), 699-717.
doi: 10.1007/s10884-008-9111-8. |
[20] |
X. Wang, X. Song, S. Tang and L. Rong, Dynamics of an HIV model with multiple infection stages and treatment with different drug classes, Bulletin of Mathematical Biology, 78 (2016), 322-349.
doi: 10.1007/s11538-016-0145-5. |
[21] |
Y. Wang, F. Brauer, J. Wu and J. M. Heffernan, A delay-dependent model with HIV drug resistance during therapy, Journal of Mathematical Analysis and Applications, 414 (2014), 514-531.
doi: 10.1016/j.jmaa.2013.12.064. |
[22] |
Z. Wang and X.-Q. Zhao, A within-host virus model with periodic multidrug therapy, Bulletin of Mathematical Biology, 75 (2013), 543-563.
doi: 10.1007/s11538-013-9820-y. |
show all references
References:
[1] |
B. Adams, H. Banks, H. Kwon and H. Tran, Dynamic multidrug therapies for HIV: Optimal and STI control approaches, Mathematical Biosciences and Engineering, 1 (2004), 223-241.
doi: 10.3934/mbe.2004.1.223. |
[2] |
N. Bacaër and S. Guernaoui, The epidemic threshold of vector-borne diseases with seasonality, Journal of Mathematical Biology, 53 (2006), 421-436.
doi: 10.1007/s00285-006-0015-0. |
[3] |
N. Bacaër and R. Ouifki, Growth rate and basic reproduction number for population models with a simple periodic factor, Mathematical Biosciences, 210 (2007), 647-658.
doi: 10.1016/j.mbs.2007.07.005. |
[4] |
N. Bacaër et al., On the biological interpretation of a definition for the parameter r 0 in periodic population models, Journal of Mathematical Biology, 65 (2012), 601-621.
doi: 10.1007/s00285-011-0479-4. |
[5] |
C. Browne, Two Extensions of a Classical Virus Model, PhD thesis, University of Florida, 2012. |
[6] |
C. J. Browne and S. S. Pilyugin, Periodic multidrug therapy in a within-host virus model, Bulletin of Mathematical Biology, 74 (2012), 562-589.
doi: 10.1007/s11538-011-9677-x. |
[7] |
C. J. Browne and S. S. Pilyugin, Global analysis of age-structured within-host virus model, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1999-2017.
doi: 10.3934/dcdsb.2013.18.1999. |
[8] |
C. J. Browne, R. J. Smith and L. Bourouiba, From regional pulse vaccination to global disease eradication: Insights from a mathematical model of poliomyelitis, Journal of Mathematical Biology, 71 (2015), 215-253.
doi: 10.1007/s00285-014-0810-y. |
[9] |
J. M. Conway and A. S. Perelson, Post-treatment control of HIV infection, Proceedings of the National Academy of Sciences, 112 (2015), 5467-5472.
doi: 10.1073/pnas.1419162112. |
[10] |
P. De Leenheer, Within-host virus models with periodic antiviral therapy, Bulletin of Mathematical Biology, 71 (2009), 189-210.
doi: 10.1007/s11538-008-9359-5. |
[11] |
P. De Leenheer and S. S. Pilyugin, Multistrain virus dynamics with mutations: A global analysis, Mathematical Medicine and Biology, 25 (2008), 285-322.
doi: 10.1093/imammb/dqn023. |
[12] |
N. M. Dixit and A. S. Perelson, Complex patterns of viral load decay under antiretroviral therapy: Influence of pharmacokinetics and intracellular delay, Journal of Theoretical Biology, 226 (2004), 95-109.
doi: 10.1016/j.jtbi.2003.09.002. |
[13] |
A. d'Onofrio, Periodically varying antiviral therapies: Conditions for global stability of the virus free state, Applied Mathematics and Computation, 168 (2005), 945-953.
doi: 10.1016/j.amc.2004.09.014. |
[14] | |
[15] |
A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Review, 41 (1999), 3-44.
doi: 10.1137/S0036144598335107. |
[16] |
L. Rong, Z. Feng and A. S. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment, Bulletin of Mathematical Biology, 69 (2007), 2027-2060.
doi: 10.1007/s11538-007-9203-3. |
[17] |
D. I. Rosenbloom, A. L. Hill, S. A. Rabi, R. F. Siliciano and M. A. Nowak, Antiretroviral dynamics determines hiv evolution and predicts therapy outcome, Nature Medicine, 18 (2012), 1378-1385.
doi: 10.1038/nm.2892. |
[18] |
H. L. Smith and P. De Leenheer, Virus dynamics: a global analysis, SIAM Journal on Applied Mathematics, 63 (2003), 1313-1327.
doi: 10.1137/S0036139902406905. |
[19] |
W. Wang and X.-Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, Journal of Dynamics and Differential Equations, 20 (2008), 699-717.
doi: 10.1007/s10884-008-9111-8. |
[20] |
X. Wang, X. Song, S. Tang and L. Rong, Dynamics of an HIV model with multiple infection stages and treatment with different drug classes, Bulletin of Mathematical Biology, 78 (2016), 322-349.
doi: 10.1007/s11538-016-0145-5. |
[21] |
Y. Wang, F. Brauer, J. Wu and J. M. Heffernan, A delay-dependent model with HIV drug resistance during therapy, Journal of Mathematical Analysis and Applications, 414 (2014), 514-531.
doi: 10.1016/j.jmaa.2013.12.064. |
[22] |
Z. Wang and X.-Q. Zhao, A within-host virus model with periodic multidrug therapy, Bulletin of Mathematical Biology, 75 (2013), 543-563.
doi: 10.1007/s11538-013-9820-y. |
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