Citation: |
[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.doi: 10.1098/rsif.2006.0112. |
[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.doi: 10.3934/mbe.2007.4.159. |
[3] |
N. Bacaër and M. G. M. Gomes, On the final size of epidemics with seasonality, Bull. Math. Biol., 71 (2009), 1954-1966.doi: 10.1007/s11538-009-9433-7. |
[4] |
F. Brauer, Some simple epidemic models, Math. Bios. Eng., 3 (2006), 1-15.doi: 10.3934/mbe.2006.3.1. |
[5] |
F. Brauer, The Kermack-McKendrick epidemic model revisited, Math. Bios., 198 (2005), 119-131.doi: 10.1016/j.mbs.2005.07.006. |
[6] |
F. Brauer, Some simple nosocomial disease transmission models, Bull. Math. Biol., 77 (2015), 460-469.doi: 10.1007/s11538-015-0061-0. |
[7] |
F. Brauer and C. Castillo-Chávez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, New York, 2001.doi: 10.1007/978-1-4757-3516-1. |
[8] |
D. L. Chao and D. T. Dimitrov, Seasonality and the effectiveness of mass vaccination, Math. Bios. Eng., 13 (2016), 249-259.doi: 10.3934/mbe.2015001. |
[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.doi: 10.1007/BF00178324. |
[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.doi: 10.1016/j.mbs.2015.05.004. |
[12] |
Z. Feng, Final and peak epidemic sizes for SEIR models with quarantine and isolation, Math. Bios. Eng., 4 (2007), 675-686.doi: 10.3934/mbe.2007.4.675. |
[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.doi: 10.1098/rspa.2012.0436. |
[14] |
Y. H. Hsieh, Pandemic influenza A (H1N1) during winter influenza season in the southern hemisphere, Infl. Other Resp. Vir. 4 (2010), 187-197.doi: 10.1111/j.1750-2659.2010.00147.x. |
[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.doi: 10.1111/tmi.12105. |
[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.doi: 10.1111/j.1365-3156.2009.02277.x. |
[18] |
Y. H. Hsieh and Y. S. Cheng, Real-time forecast of multiphase outbreak, Emerg. Infect. Dis., 12 (2006), 122-127.doi: 10.3201/eid1201.050396. |
[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.doi: 10.1186/1756-0500-3-283. |
[20] |
Y. H. Hsieh, J. Y. Lee and H. L. Chang, SARS epidemiology modeling, Emerg. Infect. Dis., 10 (2004), 1165-1167.doi: 10.3201/eid1006.031023. |
[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.doi: 10.1371/journal.pone.0111834. |
[23] |
H. Inaba, On a new perspective of the basic reproduction number in heterogeneous environments, J. Math. Biol., 65 (2012), 309-348.doi: 10.1007/s00285-011-0463-z. |
[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.doi: 10.1007/s11538-005-9047-7. |
[26] |
Z. Ma and J. Li, Dynamical Modeling and Analysis of Epidemics, Singapore, 2009.doi: 10.1142/9789812797506. |
[27] |
J. C. Miller, Epidemics on networks with large initial conditions or changing structure, PLoS ONE, 9 (2014), e101421.doi: 10.1371/journal.pone.0101421. |
[28] |
F. J. Richards, A flexible growth function for empirical use, J. Exp. Bot., 10 (1959), 290-301.doi: 10.1093/jxb/10.2.290. |
[29] |
J. V. Ross, A note on density-dependence in population models, Ecol. Model., 220 (2009), 3472-3474.doi: 10.1016/j.ecolmodel.2009.08.024. |
[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.doi: 10.1016/j.mbs.2011.09.002. |
[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.doi: 10.1016/S0025-5564(02)00108-6. |
[32] |
W. Wang and X. Q. Zhao, Basic reproduction numbers for reaction-diffusion epidemic models, SIAM J. Appl. Dyn. Syst., 11 (2012), 1652-1673.doi: 10.1137/120872942. |
[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.doi: 10.1007/s10884-013-9304-7. |
[34] |
W. Wang and X. Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Diff. Equ., 20 (2008), 699-717.doi: 10.1007/s10884-008-9111-8. |
[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.doi: 10.1016/j.jtbi.2012.07.024. |
[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.doi: 10.3934/mbe.2015.12.1055. |
[37] |
Y. Xiao, F. Brauer and S. M. Moghadas, Can treatment increase the epidemic size? J. Math. Biol., 72 (2016), 343-361.doi: 10.1007/s00285-015-0887-y. |
[38] |
X. Q. Zhao, Basic reproduction ratios for periodic compartmental models with time delay, J. Dyn. Diff. Equat., (2015), 1-16.doi: 10.1007/s10884-015-9425-2. |