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An almost periodic epidemic model in a patchy environment
1. | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China, China |
2. | School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000 |
References:
[1] |
S. Altizer, A. Dobson, P. Hosseini, P. Hudson, M. Pascual and P. Rohani, Seasonality and the dynamics of infectious diseases,, Ecology Letters, 9 (2006), 467.
doi: 10.1111/j.1461-0248.2005.00879.x. |
[2] |
J. Arino, Diseases in metapopulations. Modeling and dynamics of infectious diseases, 64-122,, Ser. Contemp. Appl. Math. CAM, (2009).
|
[3] |
G. Butler and P. Waltman, Persistence in dynamical systems,, J. Differential Equations, 63 (1986), 255.
doi: 10.1016/0022-0396(86)90049-5. |
[4] |
F. Cordova-Lepe, G. Robledo, M. Pinto and E. Gonzalez-Olivares, Modeling pulse infectious events irrupting into a controlled context: a SIS disease with almost periodic parameters,, Appl. Math. Model., 36 (2012), 1323.
doi: 10.1016/j.apm.2011.07.085. |
[5] |
C. Corduneanu, Almost Periodic Functions,, Chelsea Publishing Company New York, (1989). Google Scholar |
[6] |
S. R. Dunbar, K. P. Rybakowski and K. Schmitt, Persistence in models of predator-prey populations with diffusion,, J. Differential Equations, 65 (1986), 117.
doi: 10.1016/0022-0396(86)90044-6. |
[7] |
A. M. Fink, Almost Periodic Differential Equations,, Lecture Notes in Mathematics, (1974).
|
[8] |
D. Gao and S. Ruan, Malaria models with spatial effects, Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Disease,, D. Chen, (2014), 111. Google Scholar |
[9] |
J. K. Hale, Asymptotic Behavior of Dissipative Systems,, Math. Surveys and Monographs 25, (1988).
|
[10] |
H. W. Hethcote, Qualitative analysis of communicable disease models,, Math. Biosci., 28 (1976), 335.
doi: 10.1016/0025-5564(76)90132-2. |
[11] |
M. W. Hirsch, H. L. Smith and X.-Q. Zhao, Chain transitivity, attractivity and strong repellors for semidynamical systems,, J. Dyn. Diff. Equ., 13 (2001), 107.
doi: 10.1023/A:1009044515567. |
[12] |
X. Liu and P. Stechlinski, Transmission dynamics of a switched multi-city model with transport-related infections,, Nonlinear Anal. Real Word Appl., 14 (2013), 264.
doi: 10.1016/j.nonrwa.2012.06.003. |
[13] |
Y. Nakata, On the global stability of a delayed epidemic model with transport-related infection,, Nonlinear Anal. Real Word Appl., 12 (2011), 3028.
doi: 10.1016/j.nonrwa.2011.05.004. |
[14] |
G. Sell, Topological Dynamics and Ordinary Differential Equations,, Van Nostrand Reinhold, (1971).
|
[15] |
W. Shen and Y. Yi, Almost automorphic and almost periodic dynamics in skew-product semiflows,, Memoirs of Amer. Math. Soc., (1998).
doi: 10.1090/memo/0647. |
[16] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative systems,, Math. Surveys and Monographs, (1995).
|
[17] |
H. L. Smith and P. Waltman, The Theory of the Chemostat,, Cambridge University Press, (1995).
doi: 10.1017/CBO9780511530043. |
[18] |
B.-G. Wang and X.-Q. Zhao, Basic reproduction ratios for almost periodic compartmental epidemic models,, J. Dyn. Diff. Equ., 25 (2013), 535.
doi: 10.1007/s10884-013-9304-7. |
[19] |
W. Wang and X.-Q. Zhao, An epidemic model in a patchy environment,, Math. Biosci., 190 (2004), 97.
doi: 10.1016/j.mbs.2002.11.001. |
[20] |
W. Wang, Epidemic models with population dispersal,, Mathematics for Life Sciences and Medicine, (2007), 67.
|
[21] |
F. Zhang and X.-Q. Zhao, A periodic epidemic model in a patchy environment,, J. Math. Anal. Appl., 325 (2007), 496.
doi: 10.1016/j.jmaa.2006.01.085. |
[22] |
X.-Q. Zhao, Global attractivity and stability in some monotone discrete dynamical systems,, Bull. Austral. Math. Soc., 53 (1996), 305.
doi: 10.1017/S0004972700017032. |
[23] |
X.-Q. Zhao, Global attractivity in monotone and subhomogeneous almost periodic systems,, J. Differential Equations, 187 (2003), 494.
doi: 10.1016/S0022-0396(02)00054-2. |
[24] |
X.-Q. Zhao, Persistence in almost periodic predator-prey reaction-diffusion systems,, Fields Institute Communications, 36 (2003), 259.
|
[25] |
X.-Q. Zhao, Dynamical Systems in Population Biology,, Springer-Verlag, (2003).
doi: 10.1007/978-0-387-21761-1. |
[26] |
X.-Q. Zhao and Z. J. Jing, Global asymptotic behavior of some cooperative systems of functional differential equations,, Canad. Appl. Math. Quart., 4 (1996), 421.
|
show all references
References:
[1] |
S. Altizer, A. Dobson, P. Hosseini, P. Hudson, M. Pascual and P. Rohani, Seasonality and the dynamics of infectious diseases,, Ecology Letters, 9 (2006), 467.
doi: 10.1111/j.1461-0248.2005.00879.x. |
[2] |
J. Arino, Diseases in metapopulations. Modeling and dynamics of infectious diseases, 64-122,, Ser. Contemp. Appl. Math. CAM, (2009).
|
[3] |
G. Butler and P. Waltman, Persistence in dynamical systems,, J. Differential Equations, 63 (1986), 255.
doi: 10.1016/0022-0396(86)90049-5. |
[4] |
F. Cordova-Lepe, G. Robledo, M. Pinto and E. Gonzalez-Olivares, Modeling pulse infectious events irrupting into a controlled context: a SIS disease with almost periodic parameters,, Appl. Math. Model., 36 (2012), 1323.
doi: 10.1016/j.apm.2011.07.085. |
[5] |
C. Corduneanu, Almost Periodic Functions,, Chelsea Publishing Company New York, (1989). Google Scholar |
[6] |
S. R. Dunbar, K. P. Rybakowski and K. Schmitt, Persistence in models of predator-prey populations with diffusion,, J. Differential Equations, 65 (1986), 117.
doi: 10.1016/0022-0396(86)90044-6. |
[7] |
A. M. Fink, Almost Periodic Differential Equations,, Lecture Notes in Mathematics, (1974).
|
[8] |
D. Gao and S. Ruan, Malaria models with spatial effects, Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Disease,, D. Chen, (2014), 111. Google Scholar |
[9] |
J. K. Hale, Asymptotic Behavior of Dissipative Systems,, Math. Surveys and Monographs 25, (1988).
|
[10] |
H. W. Hethcote, Qualitative analysis of communicable disease models,, Math. Biosci., 28 (1976), 335.
doi: 10.1016/0025-5564(76)90132-2. |
[11] |
M. W. Hirsch, H. L. Smith and X.-Q. Zhao, Chain transitivity, attractivity and strong repellors for semidynamical systems,, J. Dyn. Diff. Equ., 13 (2001), 107.
doi: 10.1023/A:1009044515567. |
[12] |
X. Liu and P. Stechlinski, Transmission dynamics of a switched multi-city model with transport-related infections,, Nonlinear Anal. Real Word Appl., 14 (2013), 264.
doi: 10.1016/j.nonrwa.2012.06.003. |
[13] |
Y. Nakata, On the global stability of a delayed epidemic model with transport-related infection,, Nonlinear Anal. Real Word Appl., 12 (2011), 3028.
doi: 10.1016/j.nonrwa.2011.05.004. |
[14] |
G. Sell, Topological Dynamics and Ordinary Differential Equations,, Van Nostrand Reinhold, (1971).
|
[15] |
W. Shen and Y. Yi, Almost automorphic and almost periodic dynamics in skew-product semiflows,, Memoirs of Amer. Math. Soc., (1998).
doi: 10.1090/memo/0647. |
[16] |
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative systems,, Math. Surveys and Monographs, (1995).
|
[17] |
H. L. Smith and P. Waltman, The Theory of the Chemostat,, Cambridge University Press, (1995).
doi: 10.1017/CBO9780511530043. |
[18] |
B.-G. Wang and X.-Q. Zhao, Basic reproduction ratios for almost periodic compartmental epidemic models,, J. Dyn. Diff. Equ., 25 (2013), 535.
doi: 10.1007/s10884-013-9304-7. |
[19] |
W. Wang and X.-Q. Zhao, An epidemic model in a patchy environment,, Math. Biosci., 190 (2004), 97.
doi: 10.1016/j.mbs.2002.11.001. |
[20] |
W. Wang, Epidemic models with population dispersal,, Mathematics for Life Sciences and Medicine, (2007), 67.
|
[21] |
F. Zhang and X.-Q. Zhao, A periodic epidemic model in a patchy environment,, J. Math. Anal. Appl., 325 (2007), 496.
doi: 10.1016/j.jmaa.2006.01.085. |
[22] |
X.-Q. Zhao, Global attractivity and stability in some monotone discrete dynamical systems,, Bull. Austral. Math. Soc., 53 (1996), 305.
doi: 10.1017/S0004972700017032. |
[23] |
X.-Q. Zhao, Global attractivity in monotone and subhomogeneous almost periodic systems,, J. Differential Equations, 187 (2003), 494.
doi: 10.1016/S0022-0396(02)00054-2. |
[24] |
X.-Q. Zhao, Persistence in almost periodic predator-prey reaction-diffusion systems,, Fields Institute Communications, 36 (2003), 259.
|
[25] |
X.-Q. Zhao, Dynamical Systems in Population Biology,, Springer-Verlag, (2003).
doi: 10.1007/978-0-387-21761-1. |
[26] |
X.-Q. Zhao and Z. J. Jing, Global asymptotic behavior of some cooperative systems of functional differential equations,, Canad. Appl. Math. Quart., 4 (1996), 421.
|
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