The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence

A stochastic version of the SIS epidemic model with vaccination (SIVS) is studied. When the noise is small, the threshold parameter is identified, which determines the extinction and persistence of the epidemic. Besides, the results show that large noise will suppress the epidemic from prevailing regardless of the saturated incidence. The results are illustrated by computer simulations.

[1]  Yanan Zhao,et al.  The threshold of a stochastic SIRS epidemic model with saturated incidence , 2014, Appl. Math. Lett..

[2]  Shigui Ruan,et al.  Global analysis of an epidemic model with nonmonotone incidence rate , 2006, Mathematical Biosciences.

[3]  Aadil Lahrouz,et al.  Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence , 2013 .

[4]  G. Serio,et al.  A generalization of the Kermack-McKendrick deterministic epidemic model☆ , 1978 .

[5]  Daqing Jiang,et al.  Threshold behaviour of a stochastic SIR model , 2014 .

[6]  Pasquale Vetro,et al.  Stability of a stochastic SIR system , 2005 .

[7]  M. Zhien,et al.  Global analysis of SIS epidemic models with variable total population size , 2004 .

[8]  Daqing Jiang,et al.  Stationary distribution of a stochastic SIS epidemic model with vaccination , 2014 .

[9]  Pasquale Vetro,et al.  SIVR epidemic model with stochastic perturbation , 2012, Neural Computing and Applications.

[10]  Liangjian Hu,et al.  A Stochastic Differential Equation SIS Epidemic Model , 2011, SIAM J. Appl. Math..

[11]  R. May,et al.  Population biology of infectious diseases: Part II , 1979, Nature.

[12]  Donal O'Regan,et al.  The extinction and persistence of the stochastic SIS epidemic model with vaccination , 2013 .

[13]  Peter J. Witbooi,et al.  Stability of an SEIR epidemic model with independent stochastic perturbations , 2013 .

[14]  Henri Schurz,et al.  Stochastic Asymptotic Stability of SIR Model with Variable Diffusion Rates , 2015 .