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A mathematical model for hepatitis B with infection-age structure
1. | School of Science, Xi'an University of Technology, Xi'an 710048, China, China |
References:
[1] |
, Hepatitis B. World Health Organization Fact Sheet N$^\circ$204, World Health Organization,, 2008. Available from: , ().
|
[2] |
F. Brauer, Z. Shuai and P. van den Driessche, Dynamics of an age-of-infection cholera model, Math. Biosci. Eng., 10 (2013), 1335-1349.
doi: 10.3934/mbe.2013.10.1335. |
[3] |
D. Candotti, O. Opare-Sem, H. Rezvan, F. Sarkodie and J. P. Allain, Molecular and serological characterization of hepatitis B virus in deferred Ghanaian blood donors with and without elevated alanine aminotransferase, J. Viral. Hepat., 13 (2006), 715-724.
doi: 10.1111/j.1365-2893.2006.00741.x. |
[4] |
W. J. Edmunds, G. F. Medley, D. J. Nokes, A. J. Hall and H. C. Whittle, The influence of age on the development of the hepatitis B carrier state, Proc. R. Soc. Lond. B., 253 (1993), 197-201.
doi: 10.1098/rspb.1993.0102. |
[5] |
A. Franceschetti and A. Pugliese, Threshold behaviour of a SIR epidemic model with age structure and immigration, J. Math. Biol., 57 (2008), 1-27.
doi: 10.1007/s00285-007-0143-1. |
[6] |
D. Ganem and A. M. Prince, Hepatitis B virus infection-natural history and clinical consequences, N. Engl. J. Med., 350 (2004), 1118-1129.
doi: 10.1056/NEJMra031087. |
[7] |
J. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977. |
[8] |
J. K. Hale and P. Waltman, Persistence in infinite dimensional systems, SIAM J. Math. Anal., 20 (1989), 388-395.
doi: 10.1137/0520025. |
[9] |
G. Huang, X. Liu and Y. Takeuchi, Lyapunov functions and global stability for age-structured HIV infection model, SIAM J. Appl. Math., 72 (2012), 25-38.
doi: 10.1137/110826588. |
[10] |
H. Inaba, A semigroup approach to the strong ergodic theorem of the multistate stable population process, Math. Popul. Stud., 1 (1988), 49-77.
doi: 10.1080/08898488809525260. |
[11] |
M. Kane, Global programme for control of hepatitis B infection, Vaccine, 13 (1995), S47-S49.
doi: 10.1016/0264-410X(95)80050-N. |
[12] |
G. F. Medley, N. A. Lindop, W. J. Edmunds and D. J. Nokes, Hepatitis-B virus endemicity: Heterogeneity, catastrophic dynamics and control, Nat. Med., 7 (2001), 619-624.
doi: 10.1038/87953. |
[13] |
C. O'Leary, Z. Hong, F. Zhang, M. Dawood, G. Smart, K. Kaita and J. Wu, A Mathematical model to study the effect of hepatitis B virus vaccine and antivirus treatment among the Canadian Inuit population, Eur. J. Clin. Microbiol. Infect. Dis., 29 (2010), 63-72.
doi: 10.1007/s10096-009-0821-6. |
[14] |
P. Magal, C. C. McCluskey and G. F. Webb, Lyapunov functional and global asymptotic stability for an infection-age model, Appl. Anal., 89 (2010), 1109-1140.
doi: 10.1080/00036810903208122. |
[15] |
P. Magal and X. Q. Zhao, Global attractors in uniformlu persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), 251-275.
doi: 10.1137/S0036141003439173. |
[16] |
J. Mann and M. Roberts, Modelling the epidemiology of hepatitis B in New Zealand, J. Theor. Biol., 269 (2011), 266-272.
doi: 10.1016/j.jtbi.2010.10.028. |
[17] |
L. Rong, Z. Feng and A. S. Perelson, Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy, SIAM J. Appl. Math., 67 (2007), 731-756.
doi: 10.1137/060663945. |
[18] |
H. R. Thieme, Persistence under relaxed point-dissipativity(with application to an endemic model), SIAM J. Appl. Math., 24 (1993), 407-435.
doi: 10.1137/0524026. |
[19] |
H. R. Thieme, Semiflows generated by Lipschitz perturbation of non-densely defined operators, Diff. Integr. Equs., 3 (1990), 1035-1066. |
[20] |
S. Thornley, C. Bullen and M. Roberts, Hepatitis B in a high prevalence New Zealand population: A mathematical model applied to infection control policy, J. Theor. Biol., 254 (2008), 599-603.
doi: 10.1016/j.jtbi.2008.06.022. |
[21] |
S. X. Zhang and Y. C. Zhou, The analysis and application of an HBV model, Appl. Math. Model., 36 (2012), 1302-1312.
doi: 10.1016/j.apm.2011.07.087. |
[22] |
X. Q. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
[23] |
S. Zhao, Z. Xu and Y. Lu, A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in China, Int. J. epidemiol., 29 (1994), 744-752.
doi: 10.1093/ije/29.4.744. |
[24] |
L. Zou, S. G. Ruan and W. N. Zhang, An age-structured model for the transmission dynamics of hepatitis B, SIAM J. Appl. Math., 70 (2010), 3121-3139.
doi: 10.1137/090777645. |
[25] |
L. Zou, W. N. Zhang and S. G. Ruan, Modeling the transmission dynamics and control of hepatitis B virus in China, J. Theor. Biol., 262 (2010), 330-338.
doi: 10.1016/j.jtbi.2009.09.035. |
show all references
References:
[1] |
, Hepatitis B. World Health Organization Fact Sheet N$^\circ$204, World Health Organization,, 2008. Available from: , ().
|
[2] |
F. Brauer, Z. Shuai and P. van den Driessche, Dynamics of an age-of-infection cholera model, Math. Biosci. Eng., 10 (2013), 1335-1349.
doi: 10.3934/mbe.2013.10.1335. |
[3] |
D. Candotti, O. Opare-Sem, H. Rezvan, F. Sarkodie and J. P. Allain, Molecular and serological characterization of hepatitis B virus in deferred Ghanaian blood donors with and without elevated alanine aminotransferase, J. Viral. Hepat., 13 (2006), 715-724.
doi: 10.1111/j.1365-2893.2006.00741.x. |
[4] |
W. J. Edmunds, G. F. Medley, D. J. Nokes, A. J. Hall and H. C. Whittle, The influence of age on the development of the hepatitis B carrier state, Proc. R. Soc. Lond. B., 253 (1993), 197-201.
doi: 10.1098/rspb.1993.0102. |
[5] |
A. Franceschetti and A. Pugliese, Threshold behaviour of a SIR epidemic model with age structure and immigration, J. Math. Biol., 57 (2008), 1-27.
doi: 10.1007/s00285-007-0143-1. |
[6] |
D. Ganem and A. M. Prince, Hepatitis B virus infection-natural history and clinical consequences, N. Engl. J. Med., 350 (2004), 1118-1129.
doi: 10.1056/NEJMra031087. |
[7] |
J. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977. |
[8] |
J. K. Hale and P. Waltman, Persistence in infinite dimensional systems, SIAM J. Math. Anal., 20 (1989), 388-395.
doi: 10.1137/0520025. |
[9] |
G. Huang, X. Liu and Y. Takeuchi, Lyapunov functions and global stability for age-structured HIV infection model, SIAM J. Appl. Math., 72 (2012), 25-38.
doi: 10.1137/110826588. |
[10] |
H. Inaba, A semigroup approach to the strong ergodic theorem of the multistate stable population process, Math. Popul. Stud., 1 (1988), 49-77.
doi: 10.1080/08898488809525260. |
[11] |
M. Kane, Global programme for control of hepatitis B infection, Vaccine, 13 (1995), S47-S49.
doi: 10.1016/0264-410X(95)80050-N. |
[12] |
G. F. Medley, N. A. Lindop, W. J. Edmunds and D. J. Nokes, Hepatitis-B virus endemicity: Heterogeneity, catastrophic dynamics and control, Nat. Med., 7 (2001), 619-624.
doi: 10.1038/87953. |
[13] |
C. O'Leary, Z. Hong, F. Zhang, M. Dawood, G. Smart, K. Kaita and J. Wu, A Mathematical model to study the effect of hepatitis B virus vaccine and antivirus treatment among the Canadian Inuit population, Eur. J. Clin. Microbiol. Infect. Dis., 29 (2010), 63-72.
doi: 10.1007/s10096-009-0821-6. |
[14] |
P. Magal, C. C. McCluskey and G. F. Webb, Lyapunov functional and global asymptotic stability for an infection-age model, Appl. Anal., 89 (2010), 1109-1140.
doi: 10.1080/00036810903208122. |
[15] |
P. Magal and X. Q. Zhao, Global attractors in uniformlu persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), 251-275.
doi: 10.1137/S0036141003439173. |
[16] |
J. Mann and M. Roberts, Modelling the epidemiology of hepatitis B in New Zealand, J. Theor. Biol., 269 (2011), 266-272.
doi: 10.1016/j.jtbi.2010.10.028. |
[17] |
L. Rong, Z. Feng and A. S. Perelson, Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy, SIAM J. Appl. Math., 67 (2007), 731-756.
doi: 10.1137/060663945. |
[18] |
H. R. Thieme, Persistence under relaxed point-dissipativity(with application to an endemic model), SIAM J. Appl. Math., 24 (1993), 407-435.
doi: 10.1137/0524026. |
[19] |
H. R. Thieme, Semiflows generated by Lipschitz perturbation of non-densely defined operators, Diff. Integr. Equs., 3 (1990), 1035-1066. |
[20] |
S. Thornley, C. Bullen and M. Roberts, Hepatitis B in a high prevalence New Zealand population: A mathematical model applied to infection control policy, J. Theor. Biol., 254 (2008), 599-603.
doi: 10.1016/j.jtbi.2008.06.022. |
[21] |
S. X. Zhang and Y. C. Zhou, The analysis and application of an HBV model, Appl. Math. Model., 36 (2012), 1302-1312.
doi: 10.1016/j.apm.2011.07.087. |
[22] |
X. Q. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.
doi: 10.1007/978-0-387-21761-1. |
[23] |
S. Zhao, Z. Xu and Y. Lu, A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in China, Int. J. epidemiol., 29 (1994), 744-752.
doi: 10.1093/ije/29.4.744. |
[24] |
L. Zou, S. G. Ruan and W. N. Zhang, An age-structured model for the transmission dynamics of hepatitis B, SIAM J. Appl. Math., 70 (2010), 3121-3139.
doi: 10.1137/090777645. |
[25] |
L. Zou, W. N. Zhang and S. G. Ruan, Modeling the transmission dynamics and control of hepatitis B virus in China, J. Theor. Biol., 262 (2010), 330-338.
doi: 10.1016/j.jtbi.2009.09.035. |
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