The threshold dynamics in a stochastic SIS epidemic model with vaccination and nonlinear incidence under regime switching

2019 ◽  
Vol 529 ◽  
pp. 121555 ◽  
Author(s):  
Junna Hu ◽  
Zhidong Teng ◽  
Zhiming Li ◽  
Buyu Wen
Keyword(s):  
Epidemic Model ◽  
Regime Switching ◽  
Threshold Dynamics ◽  
Nonlinear Incidence ◽  
Sis Epidemic Model ◽  
Stochastic Sis Epidemic Model ◽  
Sis Epidemic

scholarly journals The Dynamical Behaviors in a Stochastic SIS Epidemic Model with Nonlinear Incidence

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Ramziya Rifhat ◽  
Qing Ge ◽  
Zhidong Teng
Keyword(s):  
Epidemic Model ◽  
Stochastic Perturbation ◽  
Threshold Value ◽  
Open Problems ◽  
Nonlinear Incidence ◽  
Sis Epidemic Model ◽  
Dynamical Behaviors ◽  
The Mean ◽  
Stochastic Sis Epidemic Model ◽  
Sis Epidemic

A stochastic SIS-type epidemic model with general nonlinear incidence and disease-induced mortality is investigated. It is proved that the dynamical behaviors of the model are determined by a certain threshold valueR~0. That is, whenR~0<1and together with an additional condition, the disease is extinct with probability one, and whenR~0>1, the disease is permanent in the mean in probability, and when there is not disease-related death, the disease oscillates stochastically about a positive number. Furthermore, whenR~0>1, the model admits positive recurrence and a unique stationary distribution. Particularly, the effects of the intensities of stochastic perturbation for the dynamical behaviors of the model are discussed in detail, and the dynamical behaviors for the stochastic SIS epidemic model with standard incidence are established. Finally, the numerical simulations are presented to illustrate the proposed open problems.

scholarly journals A note on the stationary distribution of stochastic SIS epidemic model with vaccination under regime switching

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4773-4785
Author(s):  
Junna Hu ◽  
Zhiming Li ◽  
Ting Zeng ◽  
Zhidong Teng
Keyword(s):  
Stationary Distribution ◽  
Epidemic Model ◽  
Regime Switching ◽  
Ergodic Property ◽  
Sis Epidemic Model ◽  
Stochastic Epidemic ◽  
A New Technique ◽  
Stochastic Sis Epidemic Model ◽  
Sis Epidemic ◽  
Stochastic Lyapunov Function

In this paper, the stochastic SIS epidemic model with vaccination under regime switching is further investigated. A new threshold Rs 0 which is different from that given in [22] is established. A new technique to deal with the nonlinear incidence and vaccination for stochastic epidemic model under regime switching is proposed. When Rs0 > 0, the existence of a unique stationary distribution and the ergodic property are obtained by constructing a new stochastic Lyapunov function with Markov switching. The corresponding result which is acquired in [22] is improved and extended.

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