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Global stability of a delayed multi-group SIRS epidemic model with nonlinear incidence rates and relapse of infection
Lyapunov functionals for virus-immune models with infinite delay
1. | Graduate School of Environmental Science, Okayama University, Okayama, 700-8530, Japan |
2. | Graduate School of Environmental and Life Science, Okayama University, Tsushimanaka 3-1-1, Okayama, 700-8530 |
3. | Graduate School of Environmental and Life Science, Okayama University, Okayama, 700-8530, Japan |
References:
[1] |
F. V. Atkinson and J. R. Haddock, On determining phase spaces for functional differential equations, Funkcial. Ekvac., 31 (1988), 331-347. |
[2] |
T. Burton and V. Hutson, Repellers in systems with infinite delay, J. Math. Anal. Appl., 137 (1989), 240-263.
doi: 10.1016/0022-247X(89)90287-4. |
[3] |
H. Gomez-Acevedo , M. Y. Li and S. Jacobson, 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. |
[4] |
J. K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21 (1978), 11-41. |
[5] |
J. K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM J. Math. Anal., 20 (1989), 388-395.
doi: 10.1137/0520025. |
[6] |
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. |
[7] |
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. |
[8] |
T. Kajiwara, T. Sasaki and Y. Takeuchi, Construction of Lyapunov functionals for delay differential equations in virology and epidemiology, Nonlinear Analysis RWA, 13 (2012), 1802-1826.
doi: 10.1016/j.nonrwa.2011.12.011. |
[9] |
T. Kajiwara, T. Sasaki and Y. Takeuchi, Construction of Lyapunov functions of the models for infectious diseases in vivo: from simple models to complex models, Math. Biosci. Eng., 12 (2015), 117-133. |
[10] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883.
doi: 10.1016/j.bulm.2004.02.001. |
[11] |
C. C. McCluskey, Global stability for an SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 6 (2009), 603-610.
doi: 10.3934/mbe.2009.6.603. |
[12] |
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. |
[13] |
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. |
[14] |
G. Röst and J. Wu, SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 5 (2008), 389-402.
doi: 10.3934/mbe.2008.5.389. |
[15] |
H. R. Thieme, Uniform weak implies uniform strong persistence for non-autonomous semiflows, Proceedings of the American Mathematical Society, 127 (1999), 2395-2403.
doi: 10.1090/S0002-9939-99-05034-0. |
[16] |
J. Wang, G. Huang and Y. Takeuchi, Global asymptotic stability for HIV-1 dynamics with two distributed delays, Mathematical Medicine and Biology, 29 (2012), 283-300.
doi: 10.1093/imammb/dqr009. |
show all references
References:
[1] |
F. V. Atkinson and J. R. Haddock, On determining phase spaces for functional differential equations, Funkcial. Ekvac., 31 (1988), 331-347. |
[2] |
T. Burton and V. Hutson, Repellers in systems with infinite delay, J. Math. Anal. Appl., 137 (1989), 240-263.
doi: 10.1016/0022-247X(89)90287-4. |
[3] |
H. Gomez-Acevedo , M. Y. Li and S. Jacobson, 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. |
[4] |
J. K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21 (1978), 11-41. |
[5] |
J. K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM J. Math. Anal., 20 (1989), 388-395.
doi: 10.1137/0520025. |
[6] |
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. |
[7] |
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. |
[8] |
T. Kajiwara, T. Sasaki and Y. Takeuchi, Construction of Lyapunov functionals for delay differential equations in virology and epidemiology, Nonlinear Analysis RWA, 13 (2012), 1802-1826.
doi: 10.1016/j.nonrwa.2011.12.011. |
[9] |
T. Kajiwara, T. Sasaki and Y. Takeuchi, Construction of Lyapunov functions of the models for infectious diseases in vivo: from simple models to complex models, Math. Biosci. Eng., 12 (2015), 117-133. |
[10] |
A. Korobeinikov, Global properties of basic virus dynamics models, Bull. Math. Biol., 66 (2004), 879-883.
doi: 10.1016/j.bulm.2004.02.001. |
[11] |
C. C. McCluskey, Global stability for an SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 6 (2009), 603-610.
doi: 10.3934/mbe.2009.6.603. |
[12] |
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. |
[13] |
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. |
[14] |
G. Röst and J. Wu, SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 5 (2008), 389-402.
doi: 10.3934/mbe.2008.5.389. |
[15] |
H. R. Thieme, Uniform weak implies uniform strong persistence for non-autonomous semiflows, Proceedings of the American Mathematical Society, 127 (1999), 2395-2403.
doi: 10.1090/S0002-9939-99-05034-0. |
[16] |
J. Wang, G. Huang and Y. Takeuchi, Global asymptotic stability for HIV-1 dynamics with two distributed delays, Mathematical Medicine and Biology, 29 (2012), 283-300.
doi: 10.1093/imammb/dqr009. |
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