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A model for disease transmission in a patchy environment
1.  Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4, Canada 
2.  Department of Mathematics and Statistics, University of Victoria, Victoria B.C., Canada V8W 3P4 
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Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete & Continuous Dynamical Systems  B, 2013, 18 (1) : 3756. doi: 10.3934/dcdsb.2013.18.37 
[2] 
Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595607. doi: 10.3934/mbe.2007.4.595 
[3] 
Gerardo Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse, J. M. Hyman. The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 14551474. doi: 10.3934/mbe.2013.10.1455 
[4] 
Tianhui Yang, Lei Zhang. Remarks on basic reproduction ratios for periodic abstract functional differential equations. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 112. doi: 10.3934/dcdsb.2019166 
[5] 
Scott W. Hansen. Controllability of a basic cochlea model. Evolution Equations & Control Theory, 2016, 5 (4) : 475487. doi: 10.3934/eect.2016015 
[6] 
Zhiting Xu. Traveling waves in an SEIR epidemic model with the variable total population. Discrete & Continuous Dynamical Systems  B, 2016, 21 (10) : 37233742. doi: 10.3934/dcdsb.2016118 
[7] 
Toshikazu Kuniya, Yoshiaki Muroya. Global stability of a multigroup SIS epidemic model for population migration. Discrete & Continuous Dynamical Systems  B, 2014, 19 (4) : 11051118. doi: 10.3934/dcdsb.2014.19.1105 
[8] 
Yanan Zhao, Daqing Jiang, Xuerong Mao, Alison Gray. The threshold of a stochastic SIRS epidemic model in a population with varying size. Discrete & Continuous Dynamical Systems  B, 2015, 20 (4) : 12771295. doi: 10.3934/dcdsb.2015.20.1277 
[9] 
Tom Burr, Gerardo Chowell. The reproduction number $R_t$ in structured and nonstructured populations. Mathematical Biosciences & Engineering, 2009, 6 (2) : 239259. doi: 10.3934/mbe.2009.6.239 
[10] 
Ling Xue, Caterina Scoglio. Networklevel reproduction number and extinction threshold for vectorborne diseases. Mathematical Biosciences & Engineering, 2015, 12 (3) : 565584. doi: 10.3934/mbe.2015.12.565 
[11] 
Gerardo Chowell, Catherine E. Ammon, Nicolas W. Hengartner, James M. Hyman. Estimating the reproduction number from the initial phase of the Spanish flu pandemic waves in Geneva, Switzerland. Mathematical Biosciences & Engineering, 2007, 4 (3) : 457470. doi: 10.3934/mbe.2007.4.457 
[12] 
Leonid A. Bunimovich. Dynamical systems and operations research: A basic model. Discrete & Continuous Dynamical Systems  B, 2001, 1 (2) : 209218. doi: 10.3934/dcdsb.2001.1.209 
[13] 
Theodore E. Galanthay. Mathematical study of the effects of travel costs on optimal dispersal in a twopatch model. Discrete & Continuous Dynamical Systems  B, 2015, 20 (6) : 16251638. doi: 10.3934/dcdsb.2015.20.1625 
[14] 
John Cleveland. Basic stage structure measure valued evolutionary game model. Mathematical Biosciences & Engineering, 2015, 12 (2) : 291310. doi: 10.3934/mbe.2015.12.291 
[15] 
XiaoQiang Zhao, Wendi Wang. Fisher waves in an epidemic model. Discrete & Continuous Dynamical Systems  B, 2004, 4 (4) : 11171128. doi: 10.3934/dcdsb.2004.4.1117 
[16] 
Jianquan Li, Zhien Ma. Stability analysis for SIS epidemic models with vaccination and constant population size. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 635642. doi: 10.3934/dcdsb.2004.4.635 
[17] 
Andreas Widder, Christian Kuehn. Heterogeneous population dynamics and scaling laws near epidemic outbreaks. Mathematical Biosciences & Engineering, 2016, 13 (5) : 10931118. doi: 10.3934/mbe.2016032 
[18] 
Hongying Shu, XiangSheng Wang. Global dynamics of a coupled epidemic model. Discrete & Continuous Dynamical Systems  B, 2017, 22 (4) : 15751585. doi: 10.3934/dcdsb.2017076 
[19] 
F. Berezovskaya, G. Karev, Baojun Song, Carlos CastilloChavez. A Simple Epidemic Model with Surprising Dynamics. Mathematical Biosciences & Engineering, 2005, 2 (1) : 133152. doi: 10.3934/mbe.2005.2.133 
[20] 
Elisabeth Logak, Isabelle Passat. An epidemic model with nonlocal diffusion on networks. Networks & Heterogeneous Media, 2016, 11 (4) : 693719. doi: 10.3934/nhm.2016014 
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