Mathematical Biosciences and Engineering (MBE)

Dynamics of epidemic models with asymptomatic infection and seasonal succession
Pages: 1407 - 1424, Issue 5/6, October/December 2017

doi:10.3934/mbe.2017073      Abstract        References        Full text (476.4K)           Related Articles

Yilei Tang - School of Mathematical Science, Shanghai Jiao Tong University, Shanghai 200240, China (email)
Dongmei Xiao - School of Mathematical Science, Shanghai Jiao Tong University, Shanghai 200240, China (email)
Weinian Zhang - Yangtze Center of Mathematics and Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China (email)
Di Zhu - School of Mathematical Science, Shanghai Jiao Tong University, Shanghai 200240, China (email)

1 M. E. Alexander and S. M. Moghadas, Bifurcation analysis of SIRS epidemic model with generalized incidence, SIAM J. Appl. Math., 65 (2005), 1794-1816.       
2 R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, New York, 1991.
3 J. Arino, F. Brauer, P. van den Driessche, J. Watmoughd and J. Wu, A model for influenza with vaccination and antiviral treatment, J. Theor. Biol., 253 (2008), 118-130.       
4 L. Bourouiba, A. Teslya and J. Wu, Highly pathogenic avian influenza outbreak mitigated by seasonal low pathogenic strains: insights from dynamic modeling, J. Theor. Biol., 271 (2011), 181-201.       
5 F. Brauer and C. Castillo-Ch├ívez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, New York, 2001.       
6 J. M. Cushing, A juvenile-adult model with periodic vital rates, J. Math. Biol., 53 (2006), 520-539.       
7 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 themodels for infectious disease in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.       
8 K. Dietz, The incidence of infectious diseases under the influence of seasonal fluctuations, Lecture Notes in Biomath, 11 (1976), 1-15, Berlin-Heidelberg-New York: Springer.
9 D. J. D. Earn, P. Rohani, B. M. Bolker and B. T. Grenfell, A simple model for complex dynamical transitions in epidemics, Science, 287 (2000), 667-670.
10 Z. Guo, L. Huang and X. Zou, Impact of discontinuous treatments on disease dynamics in an SIR epidemic model, Math. Biosci. Eng., 9 (2012), 97-110.       
11 H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599-653.       
12 Y. Hsieh, J. Liu, Y. Tzeng and J. Wu, Impact of visitors and hospital staff on nosocomial transmission and spread to community, J. Theor. Biol., 356 (2014), 20-29.       
13 W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics, Proc. R. Soc. London A: Math., 115 (1927), 700-721.
14 I. M. Longini, M. E. Halloran, A. Nizam and Y. Yang, Containing pandemic influenza with antiviral agents, Am. J. Epidemiol., 159 (2004), 623-633.
15 R. Olinky, A. Huppert and L. Stone, Seasonal dynamics and thresholds governing recurrent epidemics, J. Math. Biol. 56 (2008), 827-839.       
16 I. B. Schwartz, Small amplitude, long periodic out breaks in seasonally driven epidemics, J. Math. Biol., 30 (1992), 473-491.       
17 H. L. Smith, Multiple stable subharmonics for a periodic epidemic model, J. Math. Biol., 17 (1983), 179-190.       
18 H. L. Smith and P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge Univ. Press, 1995.       
19 L. Stone, R. Olinky and A. Huppert, Seasonal dynamics of recurrent epidemics, Nature, 446 (2007), 533-536.
20 Y. Tang, D. Huang, S. Ruan and W. Zhang, Coexistence of limit cycles and homoclinic loops in a SIRS model with a nonlinear incidence rate, SIAM J. Appl. Math., 69 (2008), 621-639.       
21 S. Towers and Z. Feng, Social contact patterns and control strategies for influenza in the elderly, Math. Biosci., 240 (2012), 241-249.       
22 S. Towers, K. Vogt Geisse, Y. Zheng and Z. Feng, Antiviral treatment for pandemic influenza: Assessing potential repercussions using a seasonally forced SIR model, J. Theor. Biol., 289 (2011), 259-268.       
23 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.       
24 W. Wang and S. Ruan, Bifurcation in an epidemic model with constant removal rate of the infectives, J. Math. Anal. Appl., 291 (2004), 775-793.       
25 W. Wang and X. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Diff. Equ., 20 (2008), 699-717.       
26 D. Xiao, Dynamics and bifurcations on a class of population model with seasonal constant-yield harvesting, Discrete Contin. Dynam. Syst. -B, 21 (2016), 699-719.       
27 D. Xiao and S. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate, Math. Biosci., 208 (2007), 419-429.       
28 F. Zhang and X. Zhao, A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), 496-516.       
29 X. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.       

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