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Global analysis of within host virus models with cell-to-cell viral transmission
1. | Department of Mathematics, University of Florida, 1400 Stadium Road, Gainesville, FL 32611, United States, United States, United States |
2. | Department of Mathematics, Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON, N2L 3C5, Canada |
References:
[1] |
W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, Heath and Co., Boston, 1965. |
[2] |
P. De Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003), 1313-1327.
doi: 10.1137/S0036139902406905. |
[3] |
P. De Leenheer and S. S. Pilyugin, Multistrain virus dynamics with mutations: A global analysis, Math. Med. Biol., 25 (2008), 285-322. |
[4] |
N. Dixit and A. Perelson, Multiplicity of human immunodeficiency virus infections in lymphoid tissue, J. Virol., 78 (2004), 8942-8945.
doi: 10.1128/JVI.78.16.8942-8945.2004. |
[5] |
M. Fiedler, Additive compound matrices and inequality for eigenvalues of stochastic matrices, Czech. Math. J., 24 (1974), 392-402. |
[6] |
H. I. Freedman, M. X. Tang and S. G. Ruan, Uniform persistence and flows near a closed positively invariant set, J. Dynam. Differential Equations, 6 (1994), 583-600.
doi: 10.1007/BF02218848. |
[7] |
H. K. Khalil, Nonlinear Systems, 3rd Edition, Prentice Hall, 2002. |
[8] |
A. Korobeinikov, Global properties of SIR and SEIR epidemic models with multiple parallel infectious stages, Bull. Math. Biol., 71 (2009), 75-83.
doi: 10.1007/s11538-008-9352-z. |
[9] |
M. Y. Li, J. R. Graef, L. Wang and J. Karsai, Global dynamics of a SEIR model with varying total population size, Math. Biosci., 160 (1999), 191-213.
doi: 10.1016/S0025-5564(99)00030-9. |
[10] |
M. Y. Li and J. S. Muldowney, A geometric approach to the global-stability problems, SIAM J. Math. Anal., 27 (1996), 1070-1083.
doi: 10.1137/S0036141094266449. |
[11] |
M. Y. Li and J. S. Muldowney, Global stability for the SEIR model in epidemiology, Math. Biosci., 125 (1995), 155-164.
doi: 10.1016/0025-5564(95)92756-5. |
[12] |
R. H. Jr. Martin, Logarithmic norms and projections applied to linear differential systems, J. Math. Anal. Appl., 45 (1974), 432-454.
doi: 10.1016/0022-247X(74)90084-5. |
[13] |
D. Mazurov, A. Ilinskaya, G. Heidecker, P. Lloyd and D. Derse, Quantitative comparison of HTLV-1 and HIV-1 Cell-to- Cell infection with new replication dependent vectors, PLoS Pathogens, 6 (2010), e1000788.
doi: 10.1371/journal.ppat.1000788. |
[14] |
B. Monel, E. Beaumont, D. Vendrame, O. Schwartz, D. Brand and F. Mammano, HIV cell-to-cell transmission requires the production of infectious virus particles and does not proceed through Env-mediated fusion pores, J. Virol., 86 (2012), 3924-3933.
doi: 10.1128/JVI.06478-11. |
[15] |
J. S. Muldowney, Compound matrices and ordinary differential equations, Rocky Mount. J. Math., 20 (1990), 857-872.
doi: 10.1216/rmjm/1181073047. |
[16] |
M. A. Nowak and R. M. May, Virus Dynamics, Oxford University press, New York, 2000. |
[17] |
A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41 (1999), 3-44.
doi: 10.1137/S0036144598335107. |
[18] |
V. Piguet and Q. Sattentau, Dangerous liaisons at the virological synapse, J. Clin. Invest., 114 (2004), 605-610.
doi: 10.1172/JCI200422812. |
[19] |
O. Schwartz, Immunological and virological aspects of HIV cell-to-cell transfer, Retrovirology, 6 (2009), I16.
doi: 10.1186/1742-4690-6-S2-I16. |
[20] |
H. L. Smith and P. Waltman, Perturbation of a globally stable steady state, Proc. Am. Math. Soc., 127 (1999), 447-453.
doi: 10.1090/S0002-9939-99-04768-1. |
[21] |
M. Sourisseau, N. Sol-Foulon, F. Porrot, F. Blanchet and O. Schwartz, Inefficient human immunodeficiency virus replication in mobile lymphocytes, J. Virol., 81 (2007), 1000-1012.
doi: 10.1128/JVI.01629-06. |
[22] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[23] |
L. Wang and S. Ellermeyer, HIV infection and $CD4^+$ T cell dynamics, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 1417-1430.
doi: 10.3934/dcdsb.2006.6.1417. |
[24] |
L. Wang and M. Y. Li, Mathematical analysis of the global dynamics of a model for HIV infection of $CD4^{+}$ T cells, Math. Biosci., 200 (2006), 44-57.
doi: 10.1016/j.mbs.2005.12.026. |
show all references
References:
[1] |
W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, Heath and Co., Boston, 1965. |
[2] |
P. De Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003), 1313-1327.
doi: 10.1137/S0036139902406905. |
[3] |
P. De Leenheer and S. S. Pilyugin, Multistrain virus dynamics with mutations: A global analysis, Math. Med. Biol., 25 (2008), 285-322. |
[4] |
N. Dixit and A. Perelson, Multiplicity of human immunodeficiency virus infections in lymphoid tissue, J. Virol., 78 (2004), 8942-8945.
doi: 10.1128/JVI.78.16.8942-8945.2004. |
[5] |
M. Fiedler, Additive compound matrices and inequality for eigenvalues of stochastic matrices, Czech. Math. J., 24 (1974), 392-402. |
[6] |
H. I. Freedman, M. X. Tang and S. G. Ruan, Uniform persistence and flows near a closed positively invariant set, J. Dynam. Differential Equations, 6 (1994), 583-600.
doi: 10.1007/BF02218848. |
[7] |
H. K. Khalil, Nonlinear Systems, 3rd Edition, Prentice Hall, 2002. |
[8] |
A. Korobeinikov, Global properties of SIR and SEIR epidemic models with multiple parallel infectious stages, Bull. Math. Biol., 71 (2009), 75-83.
doi: 10.1007/s11538-008-9352-z. |
[9] |
M. Y. Li, J. R. Graef, L. Wang and J. Karsai, Global dynamics of a SEIR model with varying total population size, Math. Biosci., 160 (1999), 191-213.
doi: 10.1016/S0025-5564(99)00030-9. |
[10] |
M. Y. Li and J. S. Muldowney, A geometric approach to the global-stability problems, SIAM J. Math. Anal., 27 (1996), 1070-1083.
doi: 10.1137/S0036141094266449. |
[11] |
M. Y. Li and J. S. Muldowney, Global stability for the SEIR model in epidemiology, Math. Biosci., 125 (1995), 155-164.
doi: 10.1016/0025-5564(95)92756-5. |
[12] |
R. H. Jr. Martin, Logarithmic norms and projections applied to linear differential systems, J. Math. Anal. Appl., 45 (1974), 432-454.
doi: 10.1016/0022-247X(74)90084-5. |
[13] |
D. Mazurov, A. Ilinskaya, G. Heidecker, P. Lloyd and D. Derse, Quantitative comparison of HTLV-1 and HIV-1 Cell-to- Cell infection with new replication dependent vectors, PLoS Pathogens, 6 (2010), e1000788.
doi: 10.1371/journal.ppat.1000788. |
[14] |
B. Monel, E. Beaumont, D. Vendrame, O. Schwartz, D. Brand and F. Mammano, HIV cell-to-cell transmission requires the production of infectious virus particles and does not proceed through Env-mediated fusion pores, J. Virol., 86 (2012), 3924-3933.
doi: 10.1128/JVI.06478-11. |
[15] |
J. S. Muldowney, Compound matrices and ordinary differential equations, Rocky Mount. J. Math., 20 (1990), 857-872.
doi: 10.1216/rmjm/1181073047. |
[16] |
M. A. Nowak and R. M. May, Virus Dynamics, Oxford University press, New York, 2000. |
[17] |
A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41 (1999), 3-44.
doi: 10.1137/S0036144598335107. |
[18] |
V. Piguet and Q. Sattentau, Dangerous liaisons at the virological synapse, J. Clin. Invest., 114 (2004), 605-610.
doi: 10.1172/JCI200422812. |
[19] |
O. Schwartz, Immunological and virological aspects of HIV cell-to-cell transfer, Retrovirology, 6 (2009), I16.
doi: 10.1186/1742-4690-6-S2-I16. |
[20] |
H. L. Smith and P. Waltman, Perturbation of a globally stable steady state, Proc. Am. Math. Soc., 127 (1999), 447-453.
doi: 10.1090/S0002-9939-99-04768-1. |
[21] |
M. Sourisseau, N. Sol-Foulon, F. Porrot, F. Blanchet and O. Schwartz, Inefficient human immunodeficiency virus replication in mobile lymphocytes, J. Virol., 81 (2007), 1000-1012.
doi: 10.1128/JVI.01629-06. |
[22] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[23] |
L. Wang and S. Ellermeyer, HIV infection and $CD4^+$ T cell dynamics, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 1417-1430.
doi: 10.3934/dcdsb.2006.6.1417. |
[24] |
L. Wang and M. Y. Li, Mathematical analysis of the global dynamics of a model for HIV infection of $CD4^{+}$ T cells, Math. Biosci., 200 (2006), 44-57.
doi: 10.1016/j.mbs.2005.12.026. |
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