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Discrete epidemic models
1.  Mathematical, Computational Modeling Sciences Center, PO Box 871904, Arizona State University, Tempe, AZ 85287, United States, United States 
2.  Department of Mathematics, Purdue University, West Lafayette, IN 47907 
[1] 
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 
[2] 
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 
[3] 
LihIng W. Roeger. Dynamically consistent discretetime SI and SIS epidemic models. Conference Publications, 2013, 2013 (special) : 653662. doi: 10.3934/proc.2013.2013.653 
[4] 
Jianquan Li, Zhien Ma, Fred Brauer. Global analysis of discretetime SI and SIS epidemic models. Mathematical Biosciences & Engineering, 2007, 4 (4) : 699710. doi: 10.3934/mbe.2007.4.699 
[5] 
Z. Feng. Final and peak epidemic sizes for SEIR models with quarantine and isolation. Mathematical Biosciences & Engineering, 2007, 4 (4) : 675686. doi: 10.3934/mbe.2007.4.675 
[6] 
Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya. Global stability for a class of discrete SIR epidemic models. Mathematical Biosciences & Engineering, 2010, 7 (2) : 347361. doi: 10.3934/mbe.2010.7.347 
[7] 
Fang Li, Nung Kwan Yip. Long time behavior of some epidemic models. Discrete & Continuous Dynamical Systems  B, 2011, 16 (3) : 867881. doi: 10.3934/dcdsb.2011.16.867 
[8] 
Fred Brauer. Some simple epidemic models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 115. doi: 10.3934/mbe.2006.3.1 
[9] 
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 
[10] 
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 
[11] 
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 
[12] 
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 
[13] 
Wendi Wang. Epidemic models with nonlinear infection forces. Mathematical Biosciences & Engineering, 2006, 3 (1) : 267279. doi: 10.3934/mbe.2006.3.267 
[14] 
Zhen Jin, Guiquan Sun, Huaiping Zhu. Epidemic models for complex networks with demographics. Mathematical Biosciences & Engineering, 2014, 11 (6) : 12951317. doi: 10.3934/mbe.2014.11.1295 
[15] 
Francisco de la Hoz, Anna Doubova, Fernando Vadillo. Persistencetime estimation for some stochastic SIS epidemic models. Discrete & Continuous Dynamical Systems  B, 2015, 20 (9) : 29332947. doi: 10.3934/dcdsb.2015.20.2933 
[16] 
W. E. Fitzgibbon, M.E. Parrott, Glenn Webb. Diffusive epidemic models with spatial and age dependent heterogeneity. Discrete & Continuous Dynamical Systems  A, 1995, 1 (1) : 3557. doi: 10.3934/dcds.1995.1.35 
[17] 
Dirk Stiefs, Ezio Venturino, Ulrike Feudel. Evidence of chaos in ecoepidemic models. Mathematical Biosciences & Engineering, 2009, 6 (4) : 855871. doi: 10.3934/mbe.2009.6.855 
[18] 
Junling Ma, Zhien Ma. Epidemic threshold conditions for seasonally forced SEIR models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 161172. doi: 10.3934/mbe.2006.3.161 
[19] 
Eunha Shim. A note on epidemic models with infective immigrants and vaccination. Mathematical Biosciences & Engineering, 2006, 3 (3) : 557566. doi: 10.3934/mbe.2006.3.557 
[20] 
Carlos M. HernándezSuárez, Carlos CastilloChavez, Osval Montesinos López, Karla HernándezCuevas. An application of queuing theory to SIS and SEIS epidemic models. Mathematical Biosciences & Engineering, 2010, 7 (4) : 809823. doi: 10.3934/mbe.2010.7.809 
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