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$R_0$ and the global behavior of an agestructured SIS epidemic model with periodicity and vertical transmission
Global dynamics for twospecies competition in patchy environment
1.  Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan, Taiwan 
2.  Department of Mathematics, Mathematical Bioscience Institute, Ohio State University, Columbus, Ohio 43210 
References:
[1] 
R. S. Cantrell, C. Cosner and Y. Lou, Evolutionary stability of ideal free dispersal strategies in patchy environments, J. Math. Biol., 65 (2012), 943965. doi: 10.1007/s0028501104865. 
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B. S. Goh, Global stability in manyspecies systems, American Naturalist, 111 (1977), 135143. doi: 10.1086/283144. 
[3] 
S. A. Gourley and Y. Kuang, Twospecies competition with high dispersal: The winning strategy, Math. Biosci. Eng., 2 (2005), 345362. doi: 10.3934/mbe.2005.2.345. 
[4] 
S. B. Hsu, H. Smith and P. Waltman, Competitive exclusion and coexistence for competitive systems on ordered Banach spaces, Trans. Amer. Math. Soc., 348 (1996), 40834094. doi: 10.1090/S0002994796017242. 
[5] 
M. Y. Li and Z. Shuai, Globalstability problem for coupled system of differential equations on networks, J. Differential Eqations., 248 (2010), 120. doi: 10.1016/j.jde.2009.09.003. 
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H. L. Smith, Competing subcommunities of mutualists and a generalized Kamke theorem, SIAM J. Appl. Math., 46 (1986), 856874. doi: 10.1137/0146052. 
[7] 
H. L. Smith, Monotone Dynamical Systems: An Introduction To The Theory of Competitive and Cooperative Systems, Math. Surveys and Monographs, Amer. Math. Soc., 1995. 
[8] 
Y. Takeuchi and Z. Lu, Permanence and global stability for competitive LotkaVolterra diffusion systems, Nonlinear Anal., 24 (1995), 91104. doi: 10.1016/0362546X(94)E0024B. 
show all references
References:
[1] 
R. S. Cantrell, C. Cosner and Y. Lou, Evolutionary stability of ideal free dispersal strategies in patchy environments, J. Math. Biol., 65 (2012), 943965. doi: 10.1007/s0028501104865. 
[2] 
B. S. Goh, Global stability in manyspecies systems, American Naturalist, 111 (1977), 135143. doi: 10.1086/283144. 
[3] 
S. A. Gourley and Y. Kuang, Twospecies competition with high dispersal: The winning strategy, Math. Biosci. Eng., 2 (2005), 345362. doi: 10.3934/mbe.2005.2.345. 
[4] 
S. B. Hsu, H. Smith and P. Waltman, Competitive exclusion and coexistence for competitive systems on ordered Banach spaces, Trans. Amer. Math. Soc., 348 (1996), 40834094. doi: 10.1090/S0002994796017242. 
[5] 
M. Y. Li and Z. Shuai, Globalstability problem for coupled system of differential equations on networks, J. Differential Eqations., 248 (2010), 120. doi: 10.1016/j.jde.2009.09.003. 
[6] 
H. L. Smith, Competing subcommunities of mutualists and a generalized Kamke theorem, SIAM J. Appl. Math., 46 (1986), 856874. doi: 10.1137/0146052. 
[7] 
H. L. Smith, Monotone Dynamical Systems: An Introduction To The Theory of Competitive and Cooperative Systems, Math. Surveys and Monographs, Amer. Math. Soc., 1995. 
[8] 
Y. Takeuchi and Z. Lu, Permanence and global stability for competitive LotkaVolterra diffusion systems, Nonlinear Anal., 24 (1995), 91104. doi: 10.1016/0362546X(94)E0024B. 
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