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Persistence in some periodic epidemic models with infection age or constant periods of infection
Asymptotic pattern of a migratory and nonmonotone population model
1. | Department of Mathematics, Foshan University, Foshan, 528000, China |
2. | Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 |
3. | Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7 |
References:
[1] |
J. Brown and N. Pavlovic, Evolution in heterogeneous environments: effects of migration on habitat specialization, Evolutionary Ecology, 6 (1992), 360-382.
doi: 10.1007/BF02270698. |
[2] |
J. Fang, J. Wei and X.-Q. Zhao, Spatial dynamics of a nonlocal and time-delayed reaction-diffusion system, J. Diff. Equations, 245 (2008), 2749-2770.
doi: 10.1016/j.jde.2008.09.001. |
[3] |
J. Fang and X.-Q. Zhao, Existence and uniqueness of traveling waves for non-monotone integral equations with applications, J. Diff. Equations, 248 (2010), 2199-2226.
doi: 10.1016/j.jde.2010.01.009. |
[4] |
S. Gourley and J. Wu, Delayed nonlocal diffusive systems in biological invasion and disease spread, Fields Inst. Commun., 48 (2006), 137-200. |
[5] |
K. Hadeler and M. Lewis, Spatial dynamics of the diffusive logistic equation with a sedentary compartment, Can. Appl. Math. Quart., 10 (2002), 473-499. |
[6] |
J. Hale, Asymptotic Behavior of Dissipative Systems, Math. surveys and monographs, Vol. 25, Amer. Math. Soc., Providence, RI, 1988. |
[7] |
S.-B. Hsu and X.-Q. Zhao, Spreading speeds and traveling wave for nonmonotone integrodifference equations, SIAM J. Math. Anal., 40 (2008), 776-789.
doi: 10.1137/070703016. |
[8] |
M. Lewis and G. Schemitz, Biological invasion of an organism with separate mobile and stationary states: Modeling and analysis, Forma, 11 (1996), 1-25. |
[9] |
R. Martin and H. Smith, Abstract functional differential equations and reaction-diffusion systems, Trans. Am. Math. Soc., 321 (1990), 1-44.
doi: 10.2307/2001590. |
[10] |
H. Smith, Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems, Math. surveys and monographs, Vol. 41, Amer. Math. Soc., Providence, RI, 1995. |
[11] |
H. Smith and X.-Q. Zhao, Robust persistence for semidynamical systems, Nonlinear Anal., 47 (2001), 6169-6179.
doi: 10.1016/S0362-546X(01)00678-2. |
[12] |
H. Thieme, Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread, J. Math. Biol., 8 (1979), 173-187.
doi: 10.1007/BF00279720. |
[13] |
H. Thieme, On a class of Hammerstein integral equations, Manuscripta Math., 29 (1979), 49-84.
doi: 10.1007/BF01309313. |
[14] |
H. Thieme and X.-Q. Zhao, A non-local delayed and diffusive predator-prey model, Nonlinear Anal. (RWA), 2 (2001), 145-160.
doi: 10.1016/S0362-546X(00)00112-7. |
[15] |
H. Thieme and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models, J. Diff. Equations, 195 (2003), 430-470.
doi: 10.1016/S0022-0396(03)00175-X. |
[16] |
Q. Wang and X.-Q. Zhao, Spreading speed and traveling waves for the diffusive logistic equation with a sedentary compartment, Dyn. Cont. Discrete Impulsive Syst. (Ser. A), 13 (2006), 231-246. |
[17] |
J. Wu, Theory and applications of partial functional differential equations, Applied Math. Sci., 119, Springer-Verlag, New York, 1996.
doi: 10.1007/978-1-4612-4050-1. |
[18] |
D. Xu and X.-Q. Zhao, A nonlocal reaction-diffusion population model with stage structure, Can. Appl. Math. Quart., 11 (2003), 303-319. |
[19] |
D. Xu and X.-Q. Zhao, Asymptotic speed of spread and traveling waves for a nonlocal epidemic model, Discrete Cont. Dyn. Syst. (Ser. B), 5 (2005), 1043-1056.
doi: 10.3934/dcdsb.2005.5.1043. |
[20] |
X.-Q. Zhao, Global attractivity in a class of nonmonotone reaction-diffusion equations with time delay, Can. Appl. Math. Quart., 17 (2009), 271-281. |
show all references
References:
[1] |
J. Brown and N. Pavlovic, Evolution in heterogeneous environments: effects of migration on habitat specialization, Evolutionary Ecology, 6 (1992), 360-382.
doi: 10.1007/BF02270698. |
[2] |
J. Fang, J. Wei and X.-Q. Zhao, Spatial dynamics of a nonlocal and time-delayed reaction-diffusion system, J. Diff. Equations, 245 (2008), 2749-2770.
doi: 10.1016/j.jde.2008.09.001. |
[3] |
J. Fang and X.-Q. Zhao, Existence and uniqueness of traveling waves for non-monotone integral equations with applications, J. Diff. Equations, 248 (2010), 2199-2226.
doi: 10.1016/j.jde.2010.01.009. |
[4] |
S. Gourley and J. Wu, Delayed nonlocal diffusive systems in biological invasion and disease spread, Fields Inst. Commun., 48 (2006), 137-200. |
[5] |
K. Hadeler and M. Lewis, Spatial dynamics of the diffusive logistic equation with a sedentary compartment, Can. Appl. Math. Quart., 10 (2002), 473-499. |
[6] |
J. Hale, Asymptotic Behavior of Dissipative Systems, Math. surveys and monographs, Vol. 25, Amer. Math. Soc., Providence, RI, 1988. |
[7] |
S.-B. Hsu and X.-Q. Zhao, Spreading speeds and traveling wave for nonmonotone integrodifference equations, SIAM J. Math. Anal., 40 (2008), 776-789.
doi: 10.1137/070703016. |
[8] |
M. Lewis and G. Schemitz, Biological invasion of an organism with separate mobile and stationary states: Modeling and analysis, Forma, 11 (1996), 1-25. |
[9] |
R. Martin and H. Smith, Abstract functional differential equations and reaction-diffusion systems, Trans. Am. Math. Soc., 321 (1990), 1-44.
doi: 10.2307/2001590. |
[10] |
H. Smith, Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems, Math. surveys and monographs, Vol. 41, Amer. Math. Soc., Providence, RI, 1995. |
[11] |
H. Smith and X.-Q. Zhao, Robust persistence for semidynamical systems, Nonlinear Anal., 47 (2001), 6169-6179.
doi: 10.1016/S0362-546X(01)00678-2. |
[12] |
H. Thieme, Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread, J. Math. Biol., 8 (1979), 173-187.
doi: 10.1007/BF00279720. |
[13] |
H. Thieme, On a class of Hammerstein integral equations, Manuscripta Math., 29 (1979), 49-84.
doi: 10.1007/BF01309313. |
[14] |
H. Thieme and X.-Q. Zhao, A non-local delayed and diffusive predator-prey model, Nonlinear Anal. (RWA), 2 (2001), 145-160.
doi: 10.1016/S0362-546X(00)00112-7. |
[15] |
H. Thieme and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models, J. Diff. Equations, 195 (2003), 430-470.
doi: 10.1016/S0022-0396(03)00175-X. |
[16] |
Q. Wang and X.-Q. Zhao, Spreading speed and traveling waves for the diffusive logistic equation with a sedentary compartment, Dyn. Cont. Discrete Impulsive Syst. (Ser. A), 13 (2006), 231-246. |
[17] |
J. Wu, Theory and applications of partial functional differential equations, Applied Math. Sci., 119, Springer-Verlag, New York, 1996.
doi: 10.1007/978-1-4612-4050-1. |
[18] |
D. Xu and X.-Q. Zhao, A nonlocal reaction-diffusion population model with stage structure, Can. Appl. Math. Quart., 11 (2003), 303-319. |
[19] |
D. Xu and X.-Q. Zhao, Asymptotic speed of spread and traveling waves for a nonlocal epidemic model, Discrete Cont. Dyn. Syst. (Ser. B), 5 (2005), 1043-1056.
doi: 10.3934/dcdsb.2005.5.1043. |
[20] |
X.-Q. Zhao, Global attractivity in a class of nonmonotone reaction-diffusion equations with time delay, Can. Appl. Math. Quart., 17 (2009), 271-281. |
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