Murray J D.Mathematical Biology[M].2nd ed.Beijing:Springer Overlag,1998.

Hethcote H W.The mathematics of infectious disease[J].SIAM Rev.,2000,42:599-653.

Capasso V,Serio G.A generalization of the Kermack-McKendrick deterministic epidemic model[J].Math.Biosci,1978,42:43-61.

Liu W M,Hethcote H W,Levin S A.Dynamical behavior of epidemiological models with nonlinear incidence rates[J].J.Math.Biol.,1987,25:359-380.

Liu W M,Levin S A,Iwasa Y.Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models[J].J.Math.Biol,1986,23:187-204.

Ruana Shigui,Wang Wendi.Dynamical behavior of an epidemic model with a nonlinear incidence rate[J].Journal of Differential Equations,2003,188:135-163.

Zhou Yugui,Xiao Dongmei,Li Yilong.Bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action[J].Chaos,Solitons and Fractals,2007,32:1903-1915.

Alexander M E,Moghadas S M.Periodicity in an epidemic model with a generalized non-linear incidence[J].Mathematical Biosciences,2004,189:75-96.

Kupiec P.Techniques for verifying the accuracy of risk measurement models[J].Journal of Derivatives,1995,3:73-84.

Zhang Xu,Liu Xianning.Backward bifurcation of an epidemic model with saturated treatment function[J].J.Math.Anal.Appl,2008,348:433-443.

Hu Zhixing,Liu Sheng,Wang Hui.Backward bifurcation of an epidemic model with standard incidence rate and treatment rate[J].Nonlinear Analysis:Real World Applications,2008,9:2302-2312.

Cui Jingan,Mu Xiaoxia,Wan Hui.Saturation recovery leads to multiple endemic equilibria and backward bifurcation[J].Journal of Theoretical Biology,2008,254:275-283.

Wang Wendi.Backward bifurcation of an epidemic model with treatment[J].Mathematical Biosciences,2006,201:58-71.