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Defining candidate drug characteristics for Long-QT (LQT3) syndrome
Sveir epidemiological model with varying infectivity and distributed delays
1. | Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China |
2. | Graduate School of Science and Technology, Shizuoka University, Hamamatsu 4328561, Japan |
3. | Graduate School of Science and Technology, Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan |
4. | Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, 3041#, 2 Yi-Kuang Street, Harbin, 150080 |
References:
[1] |
F. V. Atkinson and J. R. Haddock, On determining phase spaces for functional differential equations, Funkcial. Ekvac., 31 (1988), 331-347. |
[2] |
E. Beretta, T. Hara, W. Ma and Y. Takeuchi, Global asymptotic stability of an SIR epidemic model with distributed time delay, Nonlinear Anal., 47 (2001), 4107-4115.
doi: 10.1016/S0362-546X(01)00528-4. |
[3] |
A. B. Gumel, C. C. MuCluskey and J. Watmough, An SVEIR model for assessing potential impact of an imperfect anti-SARS vaccine, Math. Biosci. Eng., 3 (2006), 485-512. |
[4] |
A. Gabbuti, L. Romano, P. Blanc, et al., Long-term immunogenicity of hepatitis B vaccination in a cohort of Italian healthy adolescents, Vaccine, 25 (2007), 3129-3132.
doi: 10.1016/j.vaccine.2007.01.045. |
[5] |
J. K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21 (1978), 11-41. |
[6] |
Y. Hino, S. Murakami and T. Naito, "Functional-Differential Equations with Infinite Delay," Lecture Notes in Mathematics, 1473, Springer-Verlag, 1991. |
[7] |
J. R. Haddock and J. Terjéki, Liapunov-Razumikhin functions and an invariance principle for functional-differential equations, J. Differential Equations, 48 (1983), 95-122.
doi: 10.1016/0022-0396(83)90061-X. |
[8] |
J. R. Haddock, T. Krisztin and J. Terjéki, Invariance principles for autonomous functional-differential equations, J. Integral equations, 10 (1985), 123-136. |
[9] |
G. Huang, Y. Takeuchi, W. Ma and D. Wei, Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate, Bull. Math. Biol., 72 (2010), 1192-1207.
doi: 10.1007/s11538-009-9487-6. |
[10] |
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. |
[11] |
A. Korobeinikov and P. K. Maini, A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence, Math. Biosci. Eng., 1 (2004), 57-60. |
[12] |
A. Korobeinikov, Global properties of infectious disease models with nonlinear incidence, Bull. Math. Biol., 69 (2007), 1871-1886.
doi: 10.1007/s11538-007-9196-y. |
[13] |
Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics," Mathematics in Science and Engineering, 191, Academic Press, Boston, MA, 1993. |
[14] |
G. Li and Z. Jin, Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period, Chaos Solitons Fractals, 25 (2005), 1177-1184.
doi: 10.1016/j.chaos.2004.11.062. |
[15] |
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. |
[16] |
M. Y. Li and H. Shu, Impact of intracellular delays and target-cell dynamics on in vivo viral infections, SIAM J. Appl. Math., 70 (2010), 2434-2448.
doi: 10.1137/090779322. |
[17] |
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. |
[18] |
X. Liu, Y. Takeuchi and S. Iwami, SVIR epidemic models with vaccination strategies, J. Theo. Biol., 253 (2008), 1-11.
doi: 10.1016/j.jtbi.2007.10.014. |
[19] |
S. Liu and L. Wang, Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy, Math. Biosci. Eng., 7 (2010), 675-685.
doi: 10.3934/mbe.2010.7.675. |
[20] |
P. Magal, C. C. McCluskey and G. Webb, Lyapunov functional and global asymptotic stability for an infection-age model, Applicable Analysis, 89 (2010), 1109-1140.
doi: 10.1080/00036810903208122. |
[21] |
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. |
[22] |
C. C. McCluskey, Complete global stability for an SIR epidemic model with delay-distributed or discrete, Nonlinear Anal. RWA., 11 (2010), 55-59.
doi: 10.1016/j.nonrwa.2008.10.014. |
[23] |
G. Röst and J. Wu, SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 5 (2008), 389-402. |
[24] |
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. |
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] |
E. Beretta, T. Hara, W. Ma and Y. Takeuchi, Global asymptotic stability of an SIR epidemic model with distributed time delay, Nonlinear Anal., 47 (2001), 4107-4115.
doi: 10.1016/S0362-546X(01)00528-4. |
[3] |
A. B. Gumel, C. C. MuCluskey and J. Watmough, An SVEIR model for assessing potential impact of an imperfect anti-SARS vaccine, Math. Biosci. Eng., 3 (2006), 485-512. |
[4] |
A. Gabbuti, L. Romano, P. Blanc, et al., Long-term immunogenicity of hepatitis B vaccination in a cohort of Italian healthy adolescents, Vaccine, 25 (2007), 3129-3132.
doi: 10.1016/j.vaccine.2007.01.045. |
[5] |
J. K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21 (1978), 11-41. |
[6] |
Y. Hino, S. Murakami and T. Naito, "Functional-Differential Equations with Infinite Delay," Lecture Notes in Mathematics, 1473, Springer-Verlag, 1991. |
[7] |
J. R. Haddock and J. Terjéki, Liapunov-Razumikhin functions and an invariance principle for functional-differential equations, J. Differential Equations, 48 (1983), 95-122.
doi: 10.1016/0022-0396(83)90061-X. |
[8] |
J. R. Haddock, T. Krisztin and J. Terjéki, Invariance principles for autonomous functional-differential equations, J. Integral equations, 10 (1985), 123-136. |
[9] |
G. Huang, Y. Takeuchi, W. Ma and D. Wei, Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate, Bull. Math. Biol., 72 (2010), 1192-1207.
doi: 10.1007/s11538-009-9487-6. |
[10] |
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. |
[11] |
A. Korobeinikov and P. K. Maini, A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence, Math. Biosci. Eng., 1 (2004), 57-60. |
[12] |
A. Korobeinikov, Global properties of infectious disease models with nonlinear incidence, Bull. Math. Biol., 69 (2007), 1871-1886.
doi: 10.1007/s11538-007-9196-y. |
[13] |
Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics," Mathematics in Science and Engineering, 191, Academic Press, Boston, MA, 1993. |
[14] |
G. Li and Z. Jin, Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period, Chaos Solitons Fractals, 25 (2005), 1177-1184.
doi: 10.1016/j.chaos.2004.11.062. |
[15] |
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. |
[16] |
M. Y. Li and H. Shu, Impact of intracellular delays and target-cell dynamics on in vivo viral infections, SIAM J. Appl. Math., 70 (2010), 2434-2448.
doi: 10.1137/090779322. |
[17] |
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. |
[18] |
X. Liu, Y. Takeuchi and S. Iwami, SVIR epidemic models with vaccination strategies, J. Theo. Biol., 253 (2008), 1-11.
doi: 10.1016/j.jtbi.2007.10.014. |
[19] |
S. Liu and L. Wang, Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy, Math. Biosci. Eng., 7 (2010), 675-685.
doi: 10.3934/mbe.2010.7.675. |
[20] |
P. Magal, C. C. McCluskey and G. Webb, Lyapunov functional and global asymptotic stability for an infection-age model, Applicable Analysis, 89 (2010), 1109-1140.
doi: 10.1080/00036810903208122. |
[21] |
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. |
[22] |
C. C. McCluskey, Complete global stability for an SIR epidemic model with delay-distributed or discrete, Nonlinear Anal. RWA., 11 (2010), 55-59.
doi: 10.1016/j.nonrwa.2008.10.014. |
[23] |
G. Röst and J. Wu, SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 5 (2008), 389-402. |
[24] |
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. |
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