December  2011, 15(3): 915-916. doi: 10.3934/dcdsb.2011.15.915

Addendum

1. 

Department of Mathematics, Xi'an Jiaotong University, Xi'an, 710049, China

Received  December 2010 Published  February 2011

N/A.
Citation: Zhenguo Bai, Yicang Zhou. Addendum. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 915-916. doi: 10.3934/dcdsb.2011.15.915
References:
[1]

L. J. S. Allen and P. van den Driessche, The basic reproduction number in some discrete-time epidemic models,, J. Difference Equ. Appl., 14 (2008), 1127. doi: 10.1080/10236190802332308. Google Scholar

[2]

N. Bacaër, Periodic matrix population models: Growth rate, basic reproduction number, and entropy,, Bull. Math. Biol., 71 (2009), 1781. doi: 10.1007/s11538-009-9426-6. Google Scholar

[3]

N. Bacaër and S. Guernaoui, The epidemic threshold of vector-borne diseases with seasonality,, J. Math. Biol., 53 (2006), 421. doi: 10.1007/s00285-006-0015-0. Google Scholar

[4]

Z. Bai and Y. Zhou, Threshold dynamics of a bacillary dysentery model with seasonal fluctuation,, Discrete Contin. Dyn. Syst. Ser. B, 15 (2011), 1. doi: 10.3934/dcdsb.2011.15.1. Google Scholar

[5]

O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $\mathcal R_0$ in models for infectious diseases in heterogeneous populations,, J. Math. Biol., 28 (1990), 365. doi: 10.1007/BF00178324. Google Scholar

[6]

A. Fan and K. Wang, A viral infection model with immune circadian rhythms,, Appl. Math. Comput., 215 (2010), 3369. doi: 10.1016/j.amc.2009.10.028. Google Scholar

[7]

D. Greenhalgh and I. A. Moneim, SIRS epidemic model and simulations using different types of seasonal contact rate,, Syst. Anal. Model. Simulat., 43 (2003), 573. doi: 10.1080/023929021000008813. Google Scholar

[8]

Y. Lou and X.-Q. Zhao, A climate-based malaria transmission model with structured vector population,, SIAM J. Appl. Math., 70 (2010), 2023. doi: 10.1137/080744438. Google Scholar

[9]

I. A. Moneim, Seasonally varying epidemics with and without latent period: A comparative simulation study,, Math. Med. Biol., 24 (2007), 1. doi: 10.1093/imammb/dql023. Google Scholar

[10]

J. Ma and Z. Ma, Epidemic threshold conditions for seasonally forced SEIR models,, Math. Biosci. Eng., 3 (2006), 161. Google Scholar

[11]

Y. Nakata and T. Kuniya, Global dynamics of a class of SEIRS epidemic models in a periodic environment,, J. Math. Anal. Appl., 363 (2010), 230. doi: 10.1016/j.jmaa.2009.08.027. Google Scholar

[12]

H. R. Thieme, Uniform persistence and permanence for non-autonomous semiflows in population biology,, Math. Biosci., 166 (2000), 173. doi: 10.1016/S0025-5564(00)00018-3. Google Scholar

[13]

H. R. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity,, SIAM J. Appl. Math., 70 (2009), 188. doi: 10.1137/080732870. Google Scholar

[14]

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. doi: 10.1016/S0025-5564(02)00108-6. Google Scholar

[15]

C. L. Wesley and L. J. S. Allen, The basic reproduction number in epidemic models with periodic demographics,, J. Biol. Dyn., 3 (2009), 116. doi: 10.1080/17513750802304893. Google Scholar

[16]

C. L. Wesley, L. J. S. Allen and M. Langlais, Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission,, Math. Biosci. Eng., 7 (2010), 195. doi: 10.3934/mbe.2010.7.195. Google Scholar

[17]

W. Wang and X. -Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments,, J. Dyn. Diff. Equat., 20 (2008), 699. doi: 10.1007/s10884-008-9111-8. Google Scholar

show all references

References:
[1]

L. J. S. Allen and P. van den Driessche, The basic reproduction number in some discrete-time epidemic models,, J. Difference Equ. Appl., 14 (2008), 1127. doi: 10.1080/10236190802332308. Google Scholar

[2]

N. Bacaër, Periodic matrix population models: Growth rate, basic reproduction number, and entropy,, Bull. Math. Biol., 71 (2009), 1781. doi: 10.1007/s11538-009-9426-6. Google Scholar

[3]

N. Bacaër and S. Guernaoui, The epidemic threshold of vector-borne diseases with seasonality,, J. Math. Biol., 53 (2006), 421. doi: 10.1007/s00285-006-0015-0. Google Scholar

[4]

Z. Bai and Y. Zhou, Threshold dynamics of a bacillary dysentery model with seasonal fluctuation,, Discrete Contin. Dyn. Syst. Ser. B, 15 (2011), 1. doi: 10.3934/dcdsb.2011.15.1. Google Scholar

[5]

O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $\mathcal R_0$ in models for infectious diseases in heterogeneous populations,, J. Math. Biol., 28 (1990), 365. doi: 10.1007/BF00178324. Google Scholar

[6]

A. Fan and K. Wang, A viral infection model with immune circadian rhythms,, Appl. Math. Comput., 215 (2010), 3369. doi: 10.1016/j.amc.2009.10.028. Google Scholar

[7]

D. Greenhalgh and I. A. Moneim, SIRS epidemic model and simulations using different types of seasonal contact rate,, Syst. Anal. Model. Simulat., 43 (2003), 573. doi: 10.1080/023929021000008813. Google Scholar

[8]

Y. Lou and X.-Q. Zhao, A climate-based malaria transmission model with structured vector population,, SIAM J. Appl. Math., 70 (2010), 2023. doi: 10.1137/080744438. Google Scholar

[9]

I. A. Moneim, Seasonally varying epidemics with and without latent period: A comparative simulation study,, Math. Med. Biol., 24 (2007), 1. doi: 10.1093/imammb/dql023. Google Scholar

[10]

J. Ma and Z. Ma, Epidemic threshold conditions for seasonally forced SEIR models,, Math. Biosci. Eng., 3 (2006), 161. Google Scholar

[11]

Y. Nakata and T. Kuniya, Global dynamics of a class of SEIRS epidemic models in a periodic environment,, J. Math. Anal. Appl., 363 (2010), 230. doi: 10.1016/j.jmaa.2009.08.027. Google Scholar

[12]

H. R. Thieme, Uniform persistence and permanence for non-autonomous semiflows in population biology,, Math. Biosci., 166 (2000), 173. doi: 10.1016/S0025-5564(00)00018-3. Google Scholar

[13]

H. R. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity,, SIAM J. Appl. Math., 70 (2009), 188. doi: 10.1137/080732870. Google Scholar

[14]

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. doi: 10.1016/S0025-5564(02)00108-6. Google Scholar

[15]

C. L. Wesley and L. J. S. Allen, The basic reproduction number in epidemic models with periodic demographics,, J. Biol. Dyn., 3 (2009), 116. doi: 10.1080/17513750802304893. Google Scholar

[16]

C. L. Wesley, L. J. S. Allen and M. Langlais, Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission,, Math. Biosci. Eng., 7 (2010), 195. doi: 10.3934/mbe.2010.7.195. Google Scholar

[17]

W. Wang and X. -Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments,, J. Dyn. Diff. Equat., 20 (2008), 699. doi: 10.1007/s10884-008-9111-8. Google Scholar

[1]

Timothy C. Reluga, Jan Medlock, Alison Galvani. The discounted reproductive number for epidemiology. Mathematical Biosciences & Engineering, 2009, 6 (2) : 377-393. doi: 10.3934/mbe.2009.6.377

[2]

Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 37-56. doi: 10.3934/dcdsb.2013.18.37

[3]

Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595

[4]

Ariel Cintrón-Arias, Carlos Castillo-Chávez, Luís M. A. Bettencourt, Alun L. Lloyd, H. T. Banks. The estimation of the effective reproductive number from disease outbreak data. Mathematical Biosciences & Engineering, 2009, 6 (2) : 261-282. doi: 10.3934/mbe.2009.6.261

[5]

Heikki Haario, Leonid Kalachev, Marko Laine. Reduction and identification of dynamic models. Simple example: Generic receptor model. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 417-435. doi: 10.3934/dcdsb.2013.18.417

[6]

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 & Continuous Dynamical Systems - B, 2018, 23 (6) : 2153-2176. doi: 10.3934/dcdsb.2018229

[7]

Sukhitha W. Vidurupola, Linda J. S. Allen. Basic stochastic models for viral infection within a host. Mathematical Biosciences & Engineering, 2012, 9 (4) : 915-935. doi: 10.3934/mbe.2012.9.915

[8]

Fred Brauer. Some simple epidemic models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 1-15. doi: 10.3934/mbe.2006.3.1

[9]

Fred Brauer, Zhilan Feng, Carlos Castillo-Chávez. Discrete epidemic models. Mathematical Biosciences & Engineering, 2010, 7 (1) : 1-15. doi: 10.3934/mbe.2010.7.1

[10]

James M. Hyman, Jia Li. Differential susceptibility and infectivity epidemic models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 89-100. doi: 10.3934/mbe.2006.3.89

[11]

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

[12]

Qingming Gou, Wendi Wang. Global stability of two epidemic models. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 333-345. doi: 10.3934/dcdsb.2007.8.333

[13]

Linda J. S. Allen, P. van den Driessche. Stochastic epidemic models with a backward bifurcation. Mathematical Biosciences & Engineering, 2006, 3 (3) : 445-458. doi: 10.3934/mbe.2006.3.445

[14]

Wendi Wang. Epidemic models with nonlinear infection forces. Mathematical Biosciences & Engineering, 2006, 3 (1) : 267-279. doi: 10.3934/mbe.2006.3.267

[15]

Zhen Jin, Guiquan Sun, Huaiping Zhu. Epidemic models for complex networks with demographics. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1295-1317. doi: 10.3934/mbe.2014.11.1295

[16]

Dennis L. Chao, Dobromir T. Dimitrov. Seasonality and the effectiveness of mass vaccination. Mathematical Biosciences & Engineering, 2016, 13 (2) : 249-259. doi: 10.3934/mbe.2015001

[17]

Qixuan Wang, Hans G. Othmer. The performance of discrete models of low reynolds number swimmers. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1303-1320. doi: 10.3934/mbe.2015.12.1303

[18]

Gerardo Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse, J. M. Hyman. The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1455-1474. doi: 10.3934/mbe.2013.10.1455

[19]

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) : 35-57. doi: 10.3934/dcds.1995.1.35

[20]

Fang Li, Nung Kwan Yip. Long time behavior of some epidemic models. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 867-881. doi: 10.3934/dcdsb.2011.16.867

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]