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Environmental risks in a diffusive SIS model incorporating use efficiency of the medical resource
1. | School of Mathematical Science, Yangzhou University, Yangzhou 225002, China |
2. | LAboratory of Mathematical Parallel Systems (LAMPS), Centre for Disease Modeling, Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3 |
References:
[1] |
L. J. S. Allen, B. M. Bolker, Y. Lou and A. L. Nevai, Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model, Discrete Contin. Dyn. Syst. Ser. A, 21 (2008), 1-20.
doi: 10.3934/dcds.2008.21.1. |
[2] |
R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, UK, 1991. |
[3] |
R. Boaden, N. Proudlove and M. Wilson, An exploratory study of bed management, J. Manag. Med., 13 (2006), 234-250.
doi: 10.1108/02689239910292945. |
[4] |
F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, 2011.
doi: 10.1007/978-1-4614-1686-9. |
[5] |
R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, John Wiley & Sons, Ltd, 2003.
doi: 10.1002/0470871296. |
[6] |
O. Diekmann and J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases. Wiley Series in Mathematical and Computational Biology. John Wiley & Sons, West Sussex, England, 2000. |
[7] |
J. Ge, K. I. Kim, Z. G. Lin and H. P. Zhu, A SIS reaction-diffusion-advection model in a low-risk and high-risk domain, J. Differential Equations, 259 (2015), 5486-5509.
doi: 10.1016/j.jde.2015.06.035. |
[8] |
P. Hess, Periodic-parabolic Boundary Value Problems and Positivity. Pitman Research Notes in Mathematics, vol. 247. Longman Sci. Tech., Harlow, 1991. |
[9] |
W. Huang, M. Han and K. Liu, Dynamics of an SIS reaction-diffusion epidemic model for disease transmission, Math Biosci Eng., 7 (2010), 51-66.
doi: 10.3934/mbe.2010.7.51. |
[10] |
S. B. Jiang, L. Lu and L. Y. Du, Development of SARS vaccines and therapeutics is still needed, Future Virology, 8 (2013), 1-2.
doi: 10.2217/fvl.12.126. |
[11] |
K. I. Kim and Z. G. Lin, Asymptotic behavior of an SEI epidemic model with diffusion, Math. Comput. Modelling, 47 (2008), 1314-1322.
doi: 10.1016/j.mcm.2007.08.004. |
[12] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Amer.Math. Soc, Providence, RI, 1968. |
[13] |
C. C. McCluskey and Y. Yang, Global stability of a diffusive virus dynamics model with general incidence function and time delay, Nonlinear Anal. Real World Appl., 25 (2015), 64-78.
doi: 10.1016/j.nonrwa.2015.05.003. |
[14] |
R. Peng, Asymptotic profile of the positive steady state for an SIS epidemic reaction-diffusion model, I, J. Differential Equations, 247 (2009), 1096-1119.
doi: 10.1016/j.jde.2009.05.002. |
[15] |
R. Peng and F. Q. Yi, Asymptotic profile of the positive steady state for an SIS epidemic reaction-diffusion model: effects of epidemic risk and population movement, Phys. D, 259 (2013), 8-25.
doi: 10.1016/j.physd.2013.05.006. |
[16] |
R. Peng and X. Q. Zhao, A reaction-diffusion SIS epidemic model in a time-periodic environment, Nonlinearity, 25 (2012), 1451-1471.
doi: 10.1088/0951-7715/25/5/1451. |
[17] |
C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992. |
[18] |
C. H. Shan and H. P. Zhu, Bifurcations and complex dynamics of an SIR model with the impact of the number of hospital beds, J. Differential Equations, 257 (2014), 1662-1688.
doi: 10.1016/j.jde.2014.05.030. |
[19] |
C. H. Shan, Y. F. Yi and H. P. Zhu, Nilpotent singularities and dynamics in an SIR type of compartmental model with hospital resources, J. of Differential Equations, 260 (2016), 4339-4365.
doi: 10.1016/j.jde.2015.11.009. |
[20] |
Q. L. Tang, J. Ge and Z. G. Lin, An SEI-SI avian-human influenza model with diffusion and nonlocal delay, Appl. Math. Comput., 247 (2014), 753-761.
doi: 10.1016/j.amc.2014.09.042. |
[21] |
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. |
[22] |
H. Wan and H. Zhu, The backward bifurcation in compartmental models for West Nile virus, Math. Biosci., 227 (2010), 20-28.
doi: 10.1016/j.mbs.2010.05.006. |
[23] |
J. Zhou and H. W. Hethcote, Population size dependent incidence in models for diseases without immunity, J. Math. Bio., 32 (1994), 809-834.
doi: 10.1007/BF00168799. |
[24] |
, World Health Organization, World Health Statistics 2005-2011. |
[25] |
"Summary of probable SARS cases with onset of illness from 1 November 2002 to 31 July 2003"., World Health Organization (WHO). http://www.who.int/csr/sars/country/table2004_04_21/en/ |
[26] |
, http://www.who.int/management/facility/hospital/en/index6.html. |
show all references
References:
[1] |
L. J. S. Allen, B. M. Bolker, Y. Lou and A. L. Nevai, Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model, Discrete Contin. Dyn. Syst. Ser. A, 21 (2008), 1-20.
doi: 10.3934/dcds.2008.21.1. |
[2] |
R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, UK, 1991. |
[3] |
R. Boaden, N. Proudlove and M. Wilson, An exploratory study of bed management, J. Manag. Med., 13 (2006), 234-250.
doi: 10.1108/02689239910292945. |
[4] |
F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, 2011.
doi: 10.1007/978-1-4614-1686-9. |
[5] |
R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, John Wiley & Sons, Ltd, 2003.
doi: 10.1002/0470871296. |
[6] |
O. Diekmann and J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases. Wiley Series in Mathematical and Computational Biology. John Wiley & Sons, West Sussex, England, 2000. |
[7] |
J. Ge, K. I. Kim, Z. G. Lin and H. P. Zhu, A SIS reaction-diffusion-advection model in a low-risk and high-risk domain, J. Differential Equations, 259 (2015), 5486-5509.
doi: 10.1016/j.jde.2015.06.035. |
[8] |
P. Hess, Periodic-parabolic Boundary Value Problems and Positivity. Pitman Research Notes in Mathematics, vol. 247. Longman Sci. Tech., Harlow, 1991. |
[9] |
W. Huang, M. Han and K. Liu, Dynamics of an SIS reaction-diffusion epidemic model for disease transmission, Math Biosci Eng., 7 (2010), 51-66.
doi: 10.3934/mbe.2010.7.51. |
[10] |
S. B. Jiang, L. Lu and L. Y. Du, Development of SARS vaccines and therapeutics is still needed, Future Virology, 8 (2013), 1-2.
doi: 10.2217/fvl.12.126. |
[11] |
K. I. Kim and Z. G. Lin, Asymptotic behavior of an SEI epidemic model with diffusion, Math. Comput. Modelling, 47 (2008), 1314-1322.
doi: 10.1016/j.mcm.2007.08.004. |
[12] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Amer.Math. Soc, Providence, RI, 1968. |
[13] |
C. C. McCluskey and Y. Yang, Global stability of a diffusive virus dynamics model with general incidence function and time delay, Nonlinear Anal. Real World Appl., 25 (2015), 64-78.
doi: 10.1016/j.nonrwa.2015.05.003. |
[14] |
R. Peng, Asymptotic profile of the positive steady state for an SIS epidemic reaction-diffusion model, I, J. Differential Equations, 247 (2009), 1096-1119.
doi: 10.1016/j.jde.2009.05.002. |
[15] |
R. Peng and F. Q. Yi, Asymptotic profile of the positive steady state for an SIS epidemic reaction-diffusion model: effects of epidemic risk and population movement, Phys. D, 259 (2013), 8-25.
doi: 10.1016/j.physd.2013.05.006. |
[16] |
R. Peng and X. Q. Zhao, A reaction-diffusion SIS epidemic model in a time-periodic environment, Nonlinearity, 25 (2012), 1451-1471.
doi: 10.1088/0951-7715/25/5/1451. |
[17] |
C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992. |
[18] |
C. H. Shan and H. P. Zhu, Bifurcations and complex dynamics of an SIR model with the impact of the number of hospital beds, J. Differential Equations, 257 (2014), 1662-1688.
doi: 10.1016/j.jde.2014.05.030. |
[19] |
C. H. Shan, Y. F. Yi and H. P. Zhu, Nilpotent singularities and dynamics in an SIR type of compartmental model with hospital resources, J. of Differential Equations, 260 (2016), 4339-4365.
doi: 10.1016/j.jde.2015.11.009. |
[20] |
Q. L. Tang, J. Ge and Z. G. Lin, An SEI-SI avian-human influenza model with diffusion and nonlocal delay, Appl. Math. Comput., 247 (2014), 753-761.
doi: 10.1016/j.amc.2014.09.042. |
[21] |
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. |
[22] |
H. Wan and H. Zhu, The backward bifurcation in compartmental models for West Nile virus, Math. Biosci., 227 (2010), 20-28.
doi: 10.1016/j.mbs.2010.05.006. |
[23] |
J. Zhou and H. W. Hethcote, Population size dependent incidence in models for diseases without immunity, J. Math. Bio., 32 (1994), 809-834.
doi: 10.1007/BF00168799. |
[24] |
, World Health Organization, World Health Statistics 2005-2011. |
[25] |
"Summary of probable SARS cases with onset of illness from 1 November 2002 to 31 July 2003"., World Health Organization (WHO). http://www.who.int/csr/sars/country/table2004_04_21/en/ |
[26] |
, http://www.who.int/management/facility/hospital/en/index6.html. |
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