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Global dynamics of a general class of multi-group epidemic models with latency and relapse
Construction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex models
1. | Graduate School of Environmental and Life Sciences, Okayama University, 3-1-1, Tsushima-Naka, Okayama, Japan, Japan |
2. | College of Science and Engineering, Aoyama Gakuin University, 5-10-1, Fuchinobe, Sagamihara, Japan |
References:
[1] |
H. Gomez-Acevedo, M. Y. Li and J. Steven, Multistability in a model for CTL response to HTLV-I infection and its implications to HAM/TSP development and prevention, Bull. Math. Biol., 72 (2010), 681-696.
doi: 10.1007/s11538-009-9465-z. |
[2] |
G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model of viral infections, SIAM J. Appl. Math., 70 (2010), 2693-2708.
doi: 10.1137/090780821. |
[3] |
A. Iggidr, J-C. Kamgang, G. Sallet and J-J. Tewa, Global analysis of new malaria intrahost models with a competitive exclusion principle, SIAM J. Appl. Math., 67 (2006), 260-278.
doi: 10.1137/050643271. |
[4] |
T. Inoue, T. Kajiwara and T. Sasaki, Global stability of models of humoral immunity against multiple viral strains, J. Biol. Dyn., 4 (2010), 282-295.
doi: 10.1080/17513750903180275. |
[5] |
T. Kajiwara and T. Sasaki, Global stability of pathogen-immune dynamics with absorption, J. Biol Dyn. , 4 (2010), 258-269.
doi: 10.1080/17513750903051989. |
[6] |
T. Kajiwara, T. Sasaki and Y. Takeuchi, Construction of Lyapunov functionals for delay differential equations in virology and epidemiology, Nonl. Anal. RWA, 13 (2012), 1802-1826.
doi: 10.1016/j.nonrwa.2011.12.011. |
[7] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883.
doi: 10.1016/j.bulm.2004.02.001. |
[8] |
A. Korobeinikov, Global properties of infectious disease model with nonlinear incidence, Bull. Math. Biol., 69 (2007), 1871-1886.
doi: 10.1007/s11538-007-9196-y. |
[9] |
M. Y. Li and Z. Shuai, Global-stability problem for coupled systems of differential equations on networks, J. Diff. Eq., 248 (2010), 1-20.
doi: 10.1016/j.jde.2009.09.003. |
[10] |
J. Lang and M. Y. Li, Stable and transient periodic model for CTL response to HTLV-I infection, J. Math. Biol., 65 (2012), 181-199.
doi: 10.1007/s00285-011-0455-z. |
[11] |
A. Murase, T. Sasaki and T. Kajiwara, Stability analysis of pathogen-immune interaction dynamics, J. Math. Biol., 51 (2005), 247-267.
doi: 10.1007/s00285-005-0321-y. |
[12] |
M. A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74-79.
doi: 10.1126/science.272.5258.74. |
[13] |
H. Pang, W. Wang and K. Wang, Global properties of virus dynamics with CTL immune response, Southwest China Normal Univ., 30 (2005), 797-799. |
[14] |
R. Qesmi, J. Wu, J. Wu and J. M. Heffernan, Influence of backward bifurcation in a model of hepatitis B and C virus, Math. Biosc., 224 (2010), 118-125.
doi: 10.1016/j.mbs.2010.01.002. |
show all references
References:
[1] |
H. Gomez-Acevedo, M. Y. Li and J. Steven, Multistability in a model for CTL response to HTLV-I infection and its implications to HAM/TSP development and prevention, Bull. Math. Biol., 72 (2010), 681-696.
doi: 10.1007/s11538-009-9465-z. |
[2] |
G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model of viral infections, SIAM J. Appl. Math., 70 (2010), 2693-2708.
doi: 10.1137/090780821. |
[3] |
A. Iggidr, J-C. Kamgang, G. Sallet and J-J. Tewa, Global analysis of new malaria intrahost models with a competitive exclusion principle, SIAM J. Appl. Math., 67 (2006), 260-278.
doi: 10.1137/050643271. |
[4] |
T. Inoue, T. Kajiwara and T. Sasaki, Global stability of models of humoral immunity against multiple viral strains, J. Biol. Dyn., 4 (2010), 282-295.
doi: 10.1080/17513750903180275. |
[5] |
T. Kajiwara and T. Sasaki, Global stability of pathogen-immune dynamics with absorption, J. Biol Dyn. , 4 (2010), 258-269.
doi: 10.1080/17513750903051989. |
[6] |
T. Kajiwara, T. Sasaki and Y. Takeuchi, Construction of Lyapunov functionals for delay differential equations in virology and epidemiology, Nonl. Anal. RWA, 13 (2012), 1802-1826.
doi: 10.1016/j.nonrwa.2011.12.011. |
[7] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883.
doi: 10.1016/j.bulm.2004.02.001. |
[8] |
A. Korobeinikov, Global properties of infectious disease model with nonlinear incidence, Bull. Math. Biol., 69 (2007), 1871-1886.
doi: 10.1007/s11538-007-9196-y. |
[9] |
M. Y. Li and Z. Shuai, Global-stability problem for coupled systems of differential equations on networks, J. Diff. Eq., 248 (2010), 1-20.
doi: 10.1016/j.jde.2009.09.003. |
[10] |
J. Lang and M. Y. Li, Stable and transient periodic model for CTL response to HTLV-I infection, J. Math. Biol., 65 (2012), 181-199.
doi: 10.1007/s00285-011-0455-z. |
[11] |
A. Murase, T. Sasaki and T. Kajiwara, Stability analysis of pathogen-immune interaction dynamics, J. Math. Biol., 51 (2005), 247-267.
doi: 10.1007/s00285-005-0321-y. |
[12] |
M. A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistent viruses, Science, 272 (1996), 74-79.
doi: 10.1126/science.272.5258.74. |
[13] |
H. Pang, W. Wang and K. Wang, Global properties of virus dynamics with CTL immune response, Southwest China Normal Univ., 30 (2005), 797-799. |
[14] |
R. Qesmi, J. Wu, J. Wu and J. M. Heffernan, Influence of backward bifurcation in a model of hepatitis B and C virus, Math. Biosc., 224 (2010), 118-125.
doi: 10.1016/j.mbs.2010.01.002. |
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