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Mathematical Biosciences and Engineering (MBE)
 

Epidemic characteristics of two classic models and the dependence on the initial conditions
Pages: 999 - 1010, Issue 5, October 2016

doi:10.3934/mbe.2016027      Abstract        References        Full text (399.4K)           Related Articles

Jianquan Li - Science College, Air Force Engineering University, Xi'an 710051, China (email)
Yiqun Li - Science College, Air Force Engineering University, Xi'an 710051, China (email)
Yali Yang - College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China (email)

1 J. Arino, F. Brauer, P. van den Driessche, J. Watmough and J. Wu, Simple models for containment of a pandemic, J. R. Soc. Interface, 3 (2006), 453-457.
2 J. Arino, F. Brauer, P. van den Driessche, J. Watmough and J. Wu, A final size relation for epidemic models, Math. Bios. Eng., 4 (2007), 159-175.       
3 N. Bacaër and M. G. M. Gomes, On the final size of epidemics with seasonality, Bull. Math. Biol., 71 (2009), 1954-1966.       
4 F. Brauer, Some simple epidemic models, Math. Bios. Eng., 3 (2006), 1-15.       
5 F. Brauer, The Kermack-McKendrick epidemic model revisited, Math. Bios., 198 (2005), 119-131.       
6 F. Brauer, Some simple nosocomial disease transmission models, Bull. Math. Biol., 77 (2015), 460-469.       
7 F. Brauer and C. Castillo-Chávez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, New York, 2001.       
8 D. L. Chao and D. T. Dimitrov, Seasonality and the effectiveness of mass vaccination, Math. Bios. Eng., 13 (2016), 249-259.       
9 O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_{0}$ in the models for infectious disease in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.       
10 O. Diekmann, J. A. J. Metz and J. A. P. Heesterbeek, The legacy of Kermack and McKendrick, In: Epidemic Models: Their Structure and Relation to Data, Their Structure and Relation to Data, Cambridge University Press, 1995, 95-115.
11 A. Ed-Darraz and M. Khaladi, On the final size of epidemics in random environment, Math. Bios., 266 (2015), 10-14.       
12 Z. Feng, Final and peak epidemic sizes for SEIR models with quarantine and isolation, Math. Bios. Eng., 4 (2007), 675-686.       
13 T. House, J. V. Ross and D. Sirl, How big is an outbreak likely to be? Methods for epidemic final-size calculation, Proc. R. Soc. A, 469 (2013), 20120436, 22 pp.       
14 Y. H. Hsieh, Pandemic influenza A (H1N1) during winter influenza season in the southern hemisphere, Infl. Other Resp. Vir. 4 (2010), 187-197.
15 Y. H. Hsieh, Richards model: a simple procedure for real-time prediction of outbreak severity. In: Z. Ma, J. Wu and Y. Zhou editors, Modeling and Dynamics of Infectious Diseases, Series in Contemporary Applied Mathematics (CAM), Higher Education Press, Beijing, 2009, 216-236.       
16 Y. H. Hsieh, H. de Arazoza and R. Lounes, Temporal trends and regional variability of 2001-2002 multiwave DENV-3 epidemic in Havana City: did Hurricane Michelle contribute to its severity? Trop. Med. Int. Health., 18 (2013), 830-838.
17 Y. H. Hsieh and C. W. S. Chen, Turning points, reproduction number, and impact of climatological events for multi-wave dengue outbreaks, Trop. Med. Int. Heal., 14 (2009), 628-638.
18 Y. H. Hsieh and Y. S. Cheng, Real-time forecast of multiphase outbreak, Emerg. Infect. Dis., 12 (2006), 122-127.
19 Y. H. Hsieh, D. N. Fisman and J. Wu, On epidemic modeling in real time: An application to the 2009 novel A (H1N1) influenza outbreak in Canada, BMC Research Notes, 3 (2010), p283.
20 Y. H. Hsieh, J. Y. Lee and H. L. Chang, SARS epidemiology modeling, Emerg. Infect. Dis., 10 (2004), 1165-1167.
21 Y. H. Hsieh and S. Ma, Intervention measures, turning point, and reproduction number for dengue, Singapore, Am. J. Trop. Med. Hyg., 80 (2005), 66-71.
22 Y. H. Hsieh, J. Wu, J. Fang, Y. Yang and J. Lou, Quantification of bird-to-bird and bird-to-human infections during 2013 novel H7N9 avian influenza outbreak in China, PLoS ONE, 9 (2014), e111834.
23 H. Inaba, On a new perspective of the basic reproduction number in heterogeneous environments, J. Math. Biol., 65 (2012), 309-348.       
24 W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond. A, 115 (1927), 700-721.
25 J. Ma and D. J. D. Earn, Generality of the final size formula for an epidemic of a newly invading infectious disease, Bull. Math. Biol., 68 (2006), 679-702.       
26 Z. Ma and J. Li, Dynamical Modeling and Analysis of Epidemics, Singapore, 2009.       
27 J. C. Miller, Epidemics on networks with large initial conditions or changing structure, PLoS ONE, 9 (2014), e101421.
28 F. J. Richards, A flexible growth function for empirical use, J. Exp. Bot., 10 (1959), 290-301.
29 J. V. Ross, A note on density-dependence in population models, Ecol. Model., 220 (2009), 3472-3474.
30 I. Sazonov, M. Kelbert and M. B. Gravenor, A two-stage model for the SIR outbreak: Accounting for the discrete and stochastic nature of the epidemic at the initial contamination stage, Math. Biosci., 234 (2011), 108-117.       
31 P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.       
32 W. Wang and X. Q. Zhao, Basic reproduction numbers for reaction-diffusion epidemic models, SIAM J. Appl. Dyn. Syst., 11 (2012), 1652-1673.       
33 B. G. Wang and X. Q. Zhao, Basic reproduction ratios for almost periodic compartmental epidemic models. J. Dyn. Differ. Equ., 25 (2013), 535-562.       
34 W. Wang and X. Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Diff. Equ., 20 (2008), 699-717.       
35 X. S. Wang, J. Wu and Y. Yang, Richards model revisited: Validation by and application to infection dynamics, J. Theo. Biol., 313 (2012), 12-19.       
36 X. S. Wang and L. Zhong, Ebola outbreak in West Africa: Real-time estimation and multiple-wave prediction, Math. Bios. Eng., 12 (2015), 1055-1063.       
37 Y. Xiao, F. Brauer and S. M. Moghadas, Can treatment increase the epidemic size? J. Math. Biol., 72 (2016), 343-361.       
38 X. Q. Zhao, Basic reproduction ratios for periodic compartmental models with time delay, J. Dyn. Diff. Equat., (2015), 1-16.

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