LIU X N, TAKEUCHI Y, IWAMI S. SVIR Epidemic Models with Vaccination Strategies[J]. Journal of Theoretical Biology, 2008, 253(1): 1-11. doi: 10.1016/j.jtbi.2007.10.014
ALEXANDER M E, BOWMAN C, MOGHADAS S M, et al. A Vaccination Model for Transmission Dynamics of Influenza[J]. Siam Journal on Applied Dynamical Systems, 2004, 3(4): 503-524. doi: 10.1137/030600370
DUAN X C, YUAN S L, LI X Z. Global Stability of an SVIR Model with Age of Vaccination[J]. Applied Mathematics and Computation, 2014, 226: 528-540. doi: 10.1016/j.amc.2013.10.073
PANG J, CUI J A, ZHOU X. Dynamical Behavior of a Hepatitis B Virus Transmission Model with Vaccination[J]. Journal of Theoretical Biology, 2010, 265(4): 572-578. doi: 10.1016/j.jtbi.2010.05.038
LI X Z, ZHOU L L. Global Stability of an SEIR Epidemic Model with Vertical Transmission and Saturating Contact Rate[J]. Chaos Solitons & Fractals, 2009, 40(2): 874-884.
ARINO J, MCCLUSKEY C C, VAN DEN DRIESSCHE P. Global Results for an Epidemic Model with Vaccination That Exhibits Backward Bifurcation[J]. Siam Journal on Applied Mathematics, 2003, 64(1): 260-276. doi: 10.1137/S0036139902413829
MONEIM I A, KHALIL H A. Modelling and Simulation of the Spread of HBV Disease with Infectious Latent[J]. Applied Mathematics, 2015, 6(5): 745-753. doi: 10.4236/am.2015.65070
LIANG X F, BI S L, YANG W Z, et al. Epidemiological Serosurvey of Hepatitis B in China-Declining HBV Prevalence due to Hepatitis B Vaccination[J]. Vaccine, 2013, 31(47): 6550-6557.
VAN DEN DRIESSCHE P, WATMOUGH J. Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission[J]. Mathematical Biosciences, 2002, 180(1): 29-48.
马知恩, 周义仓, 李承治.常微分方程定性与稳定性方法[M]. 2版.北京:科学出版社, 2015.
HALE J K, VERDUYN L S M. Introduction to Functional Differential Equations[M]. Berlin: Springer Science & Business Media, 2013.