American Institute of Mathematical Sciences

Advanced
2007, 4(4): 675-686. doi: 10.3934/mbe.2007.4.675

Final and peak epidemic sizes for SEIR models with quarantine and isolation

Z. Feng 1,

1. 

Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395

Received  July 2007 Revised  August 2007 Published  August 2007

Two $SEIR$ models with quarantine and isolation are considered, in which the latent and infectious periods are assumed to have an exponential and gamma distribution, respectively. Previous studies have suggested (based on numerical observations) that a gamma distribution model (GDM) tends to predict a larger epidemic peak value and shorter duration than an exponential distribution model (EDM). By deriving analytic formulas for the maximum and final epidemic sizes of the two models, we demonstrate that either GDM or EDM may predict a larger epidemic peak or final epidemic size, depending on control measures. These formulas are helpful not only for understanding how model assumptions may affect the predictions, but also for confirming that it is important to assume realistic distributions of latent and infectious periods when the model is used for public health policy making.
Keywords: disease control., final epidemic size, peak epidemic size, infectious diseases, mathematical model.
Mathematics Subject Classification: 92D25, 92D30, 34C6.
Citation: Z. Feng. Final and peak epidemic sizes for SEIR models with quarantine and isolation. Mathematical Biosciences & Engineering, 2007, 4 (4) : 675-686. doi: 10.3934/mbe.2007.4.675
[1]

Daifeng Duan, Cuiping Wang, Yuan Yuan. Dynamical analysis in disease transmission and final epidemic size. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2021150
[2]

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) : 159-175. doi: 10.3934/mbe.2007.4.159
[3]

Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov. Optimal control for an epidemic in populations of varying size. Conference Publications, 2015, 2015 (special) : 549-561. doi: 10.3934/proc.2015.0549
[4]

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) : 1565-1583. doi: 10.3934/mbe.2017081
[5]

Luis F. Gordillo, Stephen A. Marion, Priscilla E. Greenwood. The effect of patterns of infectiousness on epidemic size. Mathematical Biosciences & Engineering, 2008, 5 (3) : 429-435. doi: 10.3934/mbe.2008.5.429
[6]

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) : 1277-1295. doi: 10.3934/dcdsb.2015.20.1277
[7]

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) : 761-784. doi: 10.3934/mbe.2014.11.761
[8]

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) : 1089-1110. doi: 10.3934/cpaa.2020050
[9]

Jianquan Li, Zhien Ma. Stability analysis for SIS epidemic models with vaccination and constant population size. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 635-642. doi: 10.3934/dcdsb.2004.4.635
[10]

Fred Brauer. Age-of-infection and the final size relation. Mathematical Biosciences & Engineering, 2008, 5 (4) : 681-690. doi: 10.3934/mbe.2008.5.681
[11]

Gang Huang, Edoardo Beretta, Yasuhiro Takeuchi. Global stability for epidemic model with constant latency and infectious periods. Mathematical Biosciences & Engineering, 2012, 9 (2) : 297-312. doi: 10.3934/mbe.2012.9.297
[12]

Edoardo Beretta, Dimitri Breda. An SEIR epidemic model with constant latency time and infectious period. Mathematical Biosciences & Engineering, 2011, 8 (4) : 931-952. doi: 10.3934/mbe.2011.8.931
[13]

Xia Wang, Shengqiang Liu. Global properties of a delayed SIR epidemic model with multiple parallel infectious stages. Mathematical Biosciences & Engineering, 2012, 9 (3) : 685-695. doi: 10.3934/mbe.2012.9.685
[14]

Federica Di Michele, Bruno Rubino, Rosella Sampalmieri. A steady-state mathematical model for an EOS capacitor: The effect of the size exclusion. Networks and Heterogeneous Media, 2016, 11 (4) : 603-625. doi: 10.3934/nhm.2016011
[15]

E. Almaraz, A. Gómez-Corral. On SIR-models with Markov-modulated events: Length of an outbreak, total size of the epidemic and number of secondary infections. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2153-2176. doi: 10.3934/dcdsb.2018229
[16]

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) : 288-300. doi: 10.3934/proc.1998.1998.288
[17]

Wenzhang Huang, Maoan Han, Kaiyu Liu. Dynamics of an SIS reaction-diffusion epidemic model for disease transmission. Mathematical Biosciences & Engineering, 2010, 7 (1) : 51-66. doi: 10.3934/mbe.2010.7.51
[18]

Zhenyuan Guo, Lihong Huang, Xingfu Zou. Impact of discontinuous treatments on disease dynamics in an SIR epidemic model. Mathematical Biosciences & Engineering, 2012, 9 (1) : 97-110. doi: 10.3934/mbe.2012.9.97
[19]

Rong Liu, Feng-Qin Zhang, Yuming Chen. Optimal contraception control for a nonlinear population model with size structure and a separable mortality. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3603-3618. doi: 10.3934/dcdsb.2016112
[20]

A. K. Misra, Anupama Sharma, Jia Li. A mathematical model for control of vector borne diseases through media campaigns. Discrete and Continuous Dynamical Systems - B, 2013, 18 (7) : 1909-1927. doi: 10.3934/dcdsb.2013.18.1909

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (441)
  • HTML views (0)
  • Cited by (40)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy