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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 
[1] 
Tianhui Yang, Ammar Qarariyah, Qigui Yang. The effect of spatial variables on the basic reproduction ratio for a reactiondiffusion epidemic model. Discrete and Continuous Dynamical Systems  B, 2022, 27 (6) : 30053017. doi: 10.3934/dcdsb.2021170 
[2] 
Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete and Continuous Dynamical Systems  B, 2013, 18 (1) : 3756. doi: 10.3934/dcdsb.2013.18.37 
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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 
[4] 
Nitu Kumari, Sumit Kumar, Sandeep Sharma, Fateh Singh, Rana Parshad. Basic reproduction number estimation and forecasting of COVID19: A case study of India, Brazil and Peru. Communications on Pure and Applied Analysis, , () : . doi: 10.3934/cpaa.2021170 
[5] 
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 
[6] 
Tianhui Yang, Lei Zhang. Remarks on basic reproduction ratios for periodic abstract functional differential equations. Discrete and Continuous Dynamical Systems  B, 2019, 24 (12) : 67716782. doi: 10.3934/dcdsb.2019166 
[7] 
Yancong Xu, Lijun Wei, Xiaoyu Jiang, Zirui Zhu. Complex dynamics of a SIRS epidemic model with the influence of hospital bed number. Discrete and Continuous Dynamical Systems  B, 2021, 26 (12) : 62296252. doi: 10.3934/dcdsb.2021016 
[8] 
Scott W. Hansen. Controllability of a basic cochlea model. Evolution Equations and Control Theory, 2016, 5 (4) : 475487. doi: 10.3934/eect.2016015 
[9] 
Zhiting Xu. Traveling waves in an SEIR epidemic model with the variable total population. Discrete and Continuous Dynamical Systems  B, 2016, 21 (10) : 37233742. doi: 10.3934/dcdsb.2016118 
[10] 
Toshikazu Kuniya, Yoshiaki Muroya. Global stability of a multigroup SIS epidemic model for population migration. Discrete and Continuous Dynamical Systems  B, 2014, 19 (4) : 11051118. doi: 10.3934/dcdsb.2014.19.1105 
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Yanan Zhao, Daqing Jiang, Xuerong Mao, Alison Gray. The threshold of a stochastic SIRS epidemic model in a population with varying size. Discrete and Continuous Dynamical Systems  B, 2015, 20 (4) : 12771295. doi: 10.3934/dcdsb.2015.20.1277 
[12] 
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 
[13] 
Attila Dénes, Gergely Röst. Single species population dynamics in seasonal environment with short reproduction period. Communications on Pure and Applied Analysis, 2021, 20 (2) : 755762. doi: 10.3934/cpaa.2020288 
[14] 
Qun Liu, Daqing Jiang. Dynamics of a multigroup SIRS epidemic model with random perturbations and varying total population size. Communications on Pure and Applied Analysis, 2020, 19 (2) : 10891110. doi: 10.3934/cpaa.2020050 
[15] 
Leonid A. Bunimovich. Dynamical systems and operations research: A basic model. Discrete and Continuous Dynamical Systems  B, 2001, 1 (2) : 209218. doi: 10.3934/dcdsb.2001.1.209 
[16] 
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 
[17] 
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 
[18] 
Theodore E. Galanthay. Mathematical study of the effects of travel costs on optimal dispersal in a twopatch model. Discrete and Continuous Dynamical Systems  B, 2015, 20 (6) : 16251638. doi: 10.3934/dcdsb.2015.20.1625 
[19] 
John Cleveland. Basic stage structure measure valued evolutionary game model. Mathematical Biosciences & Engineering, 2015, 12 (2) : 291310. doi: 10.3934/mbe.2015.12.291 
[20] 
XiaoQiang Zhao, Wendi Wang. Fisher waves in an epidemic model. Discrete and Continuous Dynamical Systems  B, 2004, 4 (4) : 11171128. doi: 10.3934/dcdsb.2004.4.1117 
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