Citation: |
[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), 1127-1147.doi: 10.1080/10236190802332308. |
[2] |
N. Bacaër, Periodic matrix population models: Growth rate, basic reproduction number, and entropy, Bull. Math. Biol., 71 (2009), 1781-1792.doi: 10.1007/s11538-009-9426-6. |
[3] |
N. Bacaër and S. Guernaoui, The epidemic threshold of vector-borne diseases with seasonality, J. Math. Biol., 53 (2006), 421-436.doi: 10.1007/s00285-006-0015-0. |
[4] |
Z. Bai and Y. Zhou, Threshold dynamics of a bacillary dysentery model with seasonal fluctuation, Discrete Contin. Dyn. Syst. Ser. B, 15 (2011), 1-14.doi: 10.3934/dcdsb.2011.15.1. |
[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), 365-382.doi: 10.1007/BF00178324. |
[6] |
A. Fan and K. Wang, A viral infection model with immune circadian rhythms, Appl. Math. Comput., 215 (2010), 3369-3374.doi: 10.1016/j.amc.2009.10.028. |
[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) 573-600.doi: 10.1080/023929021000008813. |
[8] |
Y. Lou and X.-Q. Zhao, A climate-based malaria transmission model with structured vector population, SIAM J. Appl. Math., 70 (2010), 2023-2044.doi: 10.1137/080744438. |
[9] |
I. A. Moneim, Seasonally varying epidemics with and without latent period: A comparative simulation study, Math. Med. Biol., 24 (2007), 1-15.doi: 10.1093/imammb/dql023. |
[10] |
J. Ma and Z. Ma, Epidemic threshold conditions for seasonally forced SEIR models, Math. Biosci. Eng., 3 (2006), 161-172. |
[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), 230-237.doi: 10.1016/j.jmaa.2009.08.027. |
[12] |
H. R. Thieme, Uniform persistence and permanence for non-autonomous semiflows in population biology, Math. Biosci., 166 (2000), 173-201.doi: 10.1016/S0025-5564(00)00018-3. |
[13] |
H. R. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity, SIAM J. Appl. Math., 70 (2009), 188-211.doi: 10.1137/080732870. |
[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), 29-48.doi: 10.1016/S0025-5564(02)00108-6. |
[15] |
C. L. Wesley and L. J. S. Allen, The basic reproduction number in epidemic models with periodic demographics, J. Biol. Dyn., 3 (2009), 116-129.doi: 10.1080/17513750802304893. |
[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), 195-211.doi: 10.3934/mbe.2010.7.195. |
[17] |
W. Wang and X. -Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Diff. Equat., 20 (2008), 699-717.doi: 10.1007/s10884-008-9111-8. |