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Global stability of the dengue disease transmission models
1. | School of Science, Xi'an University of Architecture & Technology, Xi'an, 710055, China |
2. | Department of Mathematics, Xinyang Normal University, Xinyang 464000, China |
References:
[1] |
S. Bhatt, P. W. Gething, O. J. Brady, et al., The global distribution and burden of dengue, Nature, 496 (2013), 504-507.
doi: 10.1038/nature12060. |
[2] |
L. Cai, S. Guo, X. Li and M. Ghosh, Global dynamics of a dengue epidemic mathematical model, Chaos, Solitons and Fractals, 42 (2009), 2297-2304.
doi: 10.1016/j.chaos.2009.03.130. |
[3] |
L. Cai, M. Martcheva and X. Li, epidemic models with age of infection, indirect transmission and incomplete treatment, Discrete and Continuous Dynamical Systems Series B, 18 (2013), 2239-2265.
doi: 10.3934/dcdsb.2013.18.2239. |
[4] |
L. Cai, M. Martcheva and X. Li, Competitive exclusion in a vector-host epidemic model with distributed delay, Journal of Biological Dynamics, 7 (2013), 47-67.
doi: 10.1080/17513758.2013.772253. |
[5] |
L. Cai, X. Li and M. Ghosh, Global dynamics of a mathematical model for HTLV-I infection of CD4+ T-cells, Appl. Math. Model., 35 (2011), 3587-3595.
doi: 10.1016/j.apm.2011.01.033. |
[6] |
CDC, Centers for disease control and prevention, Dengue Homepage, http://www.cdc.gov/Dengue/epidemiology/index.html |
[7] |
L. Esteva and C. Vargas, Coexistence of different serotypes of dengue virus, J. Math. Biol., 46 (2003), 31-47.
doi: 10.1007/s00285-002-0168-4. |
[8] |
Z. Feng and X. Jorge Velasco-Hernandez, Competitive exclusion in a vector-host model for the dengue fever, J. Math. Biol., 35 (1997), 523-544.
doi: 10.1007/s002850050064. |
[9] |
S. M. Garba, A. B. Gumel and M. R. Abu Bakar, Backward bifurcations in dengue transmission dynamics, Math. Biosci., 215 (2008), 11-25.
doi: 10.1016/j.mbs.2008.05.002. |
[10] |
S. B. Halstead, Pathogenesis of dengue: Challenges to molecular biology, Science, 239 (1988), 476-481.
doi: 10.1126/science.3277268. |
[11] |
J. Hofbauer and J. W.-H. So, Uniform persistence and repellors for maps, Proceedings of the American Mathematical Society, 107 (1989), 1137-1142.
doi: 10.1090/S0002-9939-1989-0984816-4. |
[12] |
D. Kalajdzievska and M. Y. Li, Modeling the effects of carriers on transmission dynamics of infectious diseases, Math. Biosci. Eng., 8 (2011), 711-722.
doi: 10.3934/mbe.2011.8.711. |
[13] |
M. Y. Li and J. S. Muldowney, A geometric approach to global-stability problems, SIAM J. Math. Anal., 27 (1996), 1070-1083.
doi: 10.1137/S0036141094266449. |
[14] |
J. Li, Y. Xiao, F. Zhang and Y. Yang, An algebraic approach to proving the global stability of a class of epidemic models, Nonlinear Anal. RWA., 13 (2012), 2006-2016.
doi: 10.1016/j.nonrwa.2011.12.022. |
[15] |
Z. Ma, Y. Zhou, W. Wang and Z. Jin, Mathematical Models and Dynamics of Infectious Diseases, China Sciences Press, Beijing, 2004. |
[16] |
C. C. McCluskey, Complete global stability for an SIR epidemic model with delay-distributed or discrete, Nonlinear Anal: Real World Appl., 11 (2010), 55-59.
doi: 10.1016/j.nonrwa.2008.10.014. |
[17] |
P. Pongsumpun and I. M. Tang, Transmission of dengue hemorrhagic fever in an age structured population, Math. Comput. Model., 37 (2003), 949-961.
doi: 10.1016/S0895-7177(03)00111-0. |
[18] |
A. J. Tatem, S. I. Hay and D. J. Rogers, Global traffic and disease vector dispersal, Proc. Natl. Acad. Sci. USA., 103 (2006), 6242-6247.
doi: 10.1073/pnas.0508391103. |
[19] |
H. R. Thieme, Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM J. Math. Anal., 24 (1993), 407-435.
doi: 10.1137/0524026. |
[20] |
H. M. Yang and C. P. Ferreira, Assessing the effects of vector control on dengue transmission, Appl. Math. Computat., 198 (2008), 401-413.
doi: 10.1016/j.amc.2007.08.046. |
show all references
References:
[1] |
S. Bhatt, P. W. Gething, O. J. Brady, et al., The global distribution and burden of dengue, Nature, 496 (2013), 504-507.
doi: 10.1038/nature12060. |
[2] |
L. Cai, S. Guo, X. Li and M. Ghosh, Global dynamics of a dengue epidemic mathematical model, Chaos, Solitons and Fractals, 42 (2009), 2297-2304.
doi: 10.1016/j.chaos.2009.03.130. |
[3] |
L. Cai, M. Martcheva and X. Li, epidemic models with age of infection, indirect transmission and incomplete treatment, Discrete and Continuous Dynamical Systems Series B, 18 (2013), 2239-2265.
doi: 10.3934/dcdsb.2013.18.2239. |
[4] |
L. Cai, M. Martcheva and X. Li, Competitive exclusion in a vector-host epidemic model with distributed delay, Journal of Biological Dynamics, 7 (2013), 47-67.
doi: 10.1080/17513758.2013.772253. |
[5] |
L. Cai, X. Li and M. Ghosh, Global dynamics of a mathematical model for HTLV-I infection of CD4+ T-cells, Appl. Math. Model., 35 (2011), 3587-3595.
doi: 10.1016/j.apm.2011.01.033. |
[6] |
CDC, Centers for disease control and prevention, Dengue Homepage, http://www.cdc.gov/Dengue/epidemiology/index.html |
[7] |
L. Esteva and C. Vargas, Coexistence of different serotypes of dengue virus, J. Math. Biol., 46 (2003), 31-47.
doi: 10.1007/s00285-002-0168-4. |
[8] |
Z. Feng and X. Jorge Velasco-Hernandez, Competitive exclusion in a vector-host model for the dengue fever, J. Math. Biol., 35 (1997), 523-544.
doi: 10.1007/s002850050064. |
[9] |
S. M. Garba, A. B. Gumel and M. R. Abu Bakar, Backward bifurcations in dengue transmission dynamics, Math. Biosci., 215 (2008), 11-25.
doi: 10.1016/j.mbs.2008.05.002. |
[10] |
S. B. Halstead, Pathogenesis of dengue: Challenges to molecular biology, Science, 239 (1988), 476-481.
doi: 10.1126/science.3277268. |
[11] |
J. Hofbauer and J. W.-H. So, Uniform persistence and repellors for maps, Proceedings of the American Mathematical Society, 107 (1989), 1137-1142.
doi: 10.1090/S0002-9939-1989-0984816-4. |
[12] |
D. Kalajdzievska and M. Y. Li, Modeling the effects of carriers on transmission dynamics of infectious diseases, Math. Biosci. Eng., 8 (2011), 711-722.
doi: 10.3934/mbe.2011.8.711. |
[13] |
M. Y. Li and J. S. Muldowney, A geometric approach to global-stability problems, SIAM J. Math. Anal., 27 (1996), 1070-1083.
doi: 10.1137/S0036141094266449. |
[14] |
J. Li, Y. Xiao, F. Zhang and Y. Yang, An algebraic approach to proving the global stability of a class of epidemic models, Nonlinear Anal. RWA., 13 (2012), 2006-2016.
doi: 10.1016/j.nonrwa.2011.12.022. |
[15] |
Z. Ma, Y. Zhou, W. Wang and Z. Jin, Mathematical Models and Dynamics of Infectious Diseases, China Sciences Press, Beijing, 2004. |
[16] |
C. C. McCluskey, Complete global stability for an SIR epidemic model with delay-distributed or discrete, Nonlinear Anal: Real World Appl., 11 (2010), 55-59.
doi: 10.1016/j.nonrwa.2008.10.014. |
[17] |
P. Pongsumpun and I. M. Tang, Transmission of dengue hemorrhagic fever in an age structured population, Math. Comput. Model., 37 (2003), 949-961.
doi: 10.1016/S0895-7177(03)00111-0. |
[18] |
A. J. Tatem, S. I. Hay and D. J. Rogers, Global traffic and disease vector dispersal, Proc. Natl. Acad. Sci. USA., 103 (2006), 6242-6247.
doi: 10.1073/pnas.0508391103. |
[19] |
H. R. Thieme, Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM J. Math. Anal., 24 (1993), 407-435.
doi: 10.1137/0524026. |
[20] |
H. M. Yang and C. P. Ferreira, Assessing the effects of vector control on dengue transmission, Appl. Math. Computat., 198 (2008), 401-413.
doi: 10.1016/j.amc.2007.08.046. |
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