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Modeling spatial spread of west nile virus and impact of directional dispersal of birds
Epidemic threshold conditions for seasonally forced SEIR models
1.  Department of Mathematics and Statistics, McMaster University, Hamilton, ON Canada L8S 4K1, Canada 
2.  Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China 
[1] 
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] 
Yilei Tang, Dongmei Xiao, Weinian Zhang, Di Zhu. Dynamics of epidemic models with asymptomatic infection and seasonal succession. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 14071424. doi: 10.3934/mbe.2017073 
[4] 
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 
[5] 
Tianhui Yang, Lei Zhang. Remarks on basic reproduction ratios for periodic abstract functional differential equations. Discrete & Continuous Dynamical Systems  B, 2019, 24 (12) : 67716782. doi: 10.3934/dcdsb.2019166 
[6] 
Jinhuo Luo, Jin Wang, Hao Wang. Seasonal forcing and exponential threshold incidence in cholera dynamics. Discrete & Continuous Dynamical Systems  B, 2017, 22 (6) : 22612290. doi: 10.3934/dcdsb.2017095 
[7] 
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 
[8] 
Xueping Li, Jingli Ren, Sue Ann Campbell, Gail S. K. Wolkowicz, Huaiping Zhu. How seasonal forcing influences the complexity of a predatorprey system. Discrete & Continuous Dynamical Systems  B, 2018, 23 (2) : 785807. doi: 10.3934/dcdsb.2018043 
[9] 
E. Almaraz, A. GómezCorral. On SIRmodels with Markovmodulated events: Length of an outbreak, total size of the epidemic and number of secondary infections. Discrete & Continuous Dynamical Systems  B, 2018, 23 (6) : 21532176. doi: 10.3934/dcdsb.2018229 
[10] 
Sukhitha W. Vidurupola, Linda J. S. Allen. Basic stochastic models for viral infection within a host. Mathematical Biosciences & Engineering, 2012, 9 (4) : 915935. doi: 10.3934/mbe.2012.9.915 
[11] 
Pierre Magal, Ahmed Noussair, Glenn Webb, Yixiang Wu. Modeling epidemic outbreaks in geographical regions: Seasonal influenza in Puerto Rico. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020237 
[12] 
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 
[13] 
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 
[14] 
Fred Brauer. Some simple epidemic models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 115. doi: 10.3934/mbe.2006.3.1 
[15] 
Fred Brauer, Zhilan Feng, Carlos CastilloChávez. Discrete epidemic models. Mathematical Biosciences & Engineering, 2010, 7 (1) : 115. doi: 10.3934/mbe.2010.7.1 
[16] 
James M. Hyman, Jia Li. Differential susceptibility and infectivity epidemic models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 89100. doi: 10.3934/mbe.2006.3.89 
[17] 
Julien Arino, Fred Brauer, P. van den Driessche, James Watmough, Jianhong Wu. A final size relation for epidemic models. Mathematical Biosciences & Engineering, 2007, 4 (2) : 159175. doi: 10.3934/mbe.2007.4.159 
[18] 
Qingming Gou, Wendi Wang. Global stability of two epidemic models. Discrete & Continuous Dynamical Systems  B, 2007, 8 (2) : 333345. doi: 10.3934/dcdsb.2007.8.333 
[19] 
Linda J. S. Allen, P. van den Driessche. Stochastic epidemic models with a backward bifurcation. Mathematical Biosciences & Engineering, 2006, 3 (3) : 445458. doi: 10.3934/mbe.2006.3.445 
[20] 
Wendi Wang. Epidemic models with nonlinear infection forces. Mathematical Biosciences & Engineering, 2006, 3 (1) : 267279. doi: 10.3934/mbe.2006.3.267 
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