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Final and peak epidemic sizes for SEIR models with quarantine and isolation
1.  Department of Mathematics, Purdue University, West Lafayette, IN 479071395 
[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] 
Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov. Optimal control for an epidemic in populations of varying size. Conference Publications, 2015, 2015 (special) : 549561. doi: 10.3934/proc.2015.0549 
[3] 
Min Zhu, Xiaofei Guo, Zhigui Lin. The risk index for an SIR epidemic model and spatial spreading of the infectious disease. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 15651583. doi: 10.3934/mbe.2017081 
[4] 
Luis F. Gordillo, Stephen A. Marion, Priscilla E. Greenwood. The effect of patterns of infectiousness on epidemic size. Mathematical Biosciences & Engineering, 2008, 5 (3) : 429435. doi: 10.3934/mbe.2008.5.429 
[5] 
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 
[6] 
M. H. A. Biswas, L. T. Paiva, MdR de Pinho. A SEIR model for control of infectious diseases with constraints. Mathematical Biosciences & Engineering, 2014, 11 (4) : 761784. doi: 10.3934/mbe.2014.11.761 
[7] 
Qun Liu, Daqing Jiang. Dynamics of a multigroup SIRS epidemic model with random perturbations and varying total population size. Communications on Pure & Applied Analysis, 2020, 19 (2) : 10891110. doi: 10.3934/cpaa.2020050 
[8] 
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 
[9] 
Fred Brauer. Ageofinfection and the final size relation. Mathematical Biosciences & Engineering, 2008, 5 (4) : 681690. doi: 10.3934/mbe.2008.5.681 
[10] 
Gang Huang, Edoardo Beretta, Yasuhiro Takeuchi. Global stability for epidemic model with constant latency and infectious periods. Mathematical Biosciences & Engineering, 2012, 9 (2) : 297312. doi: 10.3934/mbe.2012.9.297 
[11] 
Edoardo Beretta, Dimitri Breda. An SEIR epidemic model with constant latency time and infectious period. Mathematical Biosciences & Engineering, 2011, 8 (4) : 931952. doi: 10.3934/mbe.2011.8.931 
[12] 
Xia Wang, Shengqiang Liu. Global properties of a delayed SIR epidemic model with multiple parallel infectious stages. Mathematical Biosciences & Engineering, 2012, 9 (3) : 685695. doi: 10.3934/mbe.2012.9.685 
[13] 
Federica Di Michele, Bruno Rubino, Rosella Sampalmieri. A steadystate mathematical model for an EOS capacitor: The effect of the size exclusion. Networks & Heterogeneous Media, 2016, 11 (4) : 603625. doi: 10.3934/nhm.2016011 
[14] 
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 
[15] 
John R. Graef, Michael Y. Li, Liancheng Wang. A study on the effects of disease caused death in a simple epidemic model. Conference Publications, 1998, 1998 (Special) : 288300. doi: 10.3934/proc.1998.1998.288 
[16] 
Wenzhang Huang, Maoan Han, Kaiyu Liu. Dynamics of an SIS reactiondiffusion epidemic model for disease transmission. Mathematical Biosciences & Engineering, 2010, 7 (1) : 5166. doi: 10.3934/mbe.2010.7.51 
[17] 
Zhenyuan Guo, Lihong Huang, Xingfu Zou. Impact of discontinuous treatments on disease dynamics in an SIR epidemic model. Mathematical Biosciences & Engineering, 2012, 9 (1) : 97110. doi: 10.3934/mbe.2012.9.97 
[18] 
Rong Liu, FengQin Zhang, Yuming Chen. Optimal contraception control for a nonlinear population model with size structure and a separable mortality. Discrete & Continuous Dynamical Systems  B, 2016, 21 (10) : 36033618. doi: 10.3934/dcdsb.2016112 
[19] 
A. K. Misra, Anupama Sharma, Jia Li. A mathematical model for control of vector borne diseases through media campaigns. Discrete & Continuous Dynamical Systems  B, 2013, 18 (7) : 19091927. doi: 10.3934/dcdsb.2013.18.1909 
[20] 
Hongbin Guo, Michael Yi Li. Global dynamics of a staged progression model for infectious diseases. Mathematical Biosciences & Engineering, 2006, 3 (3) : 513525. doi: 10.3934/mbe.2006.3.513 
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