Asymptotic properties of a stochastic SIRS epidemic model with nonlinear incidence and varying population sizes

2019 ◽  
Vol 35 (1) ◽  
pp. 56-80 ◽  
Author(s):  
Ramziya Rifhat ◽  
Ahmadjan Muhammadhaji ◽  
Zhidong Teng
Keyword(s):  
Epidemic Model ◽  
Asymptotic Properties ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Population Sizes ◽  
Stochastic Sirs Epidemic Model ◽  
Varying Population

scholarly journals Threshold dynamics for a class of stochastic SIRS epidemic models with nonlinear incidence and Markovian switching

2021 ◽  
Author(s):  
Amine EL Koufi ◽  
Abdelkrim Bennar ◽  
Noura Yousfi ◽  
M Pitchaimani
Keyword(s):  
Numerical Simulations ◽  
Stochastic System ◽  
Epidemic Model ◽  
Stochastic Calculus ◽  
Markovian Switching ◽  
Threshold Dynamics ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Stochastic Sirs Epidemic Model ◽  
Theoretical Results

In this paper, we consider a stochastic SIRS epidemic model with nonlinear incidence and Markovian switching. By using the stochastic calculus background, we establish that the stochastic threshold R_{ swt}  can be used to determine the compartment dynamics of the stochastic system. Some examples and numerical simulations are presented to confirm the theoretical results established in this paper.

Dynamics of a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination and nonlinear incidence under regime switching and Lévy jumps

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Junna Hu ◽  
Buyu Wen ◽  
Ting Zeng ◽  
Zhidong Teng
Keyword(s):  
Epidemic Model ◽  
Regime Switching ◽  
Markov Switching ◽  
Threshold Value ◽  
Open Problems ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Stochastic Epidemic ◽  
Lévy Jumps ◽  
White Noises

Abstract In this paper, a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination, nonlinear incidence and white noises under regime switching and Lévy jumps is investigated. A new threshold value is determined. Some basic assumptions with regard to nonlinear incidence, white noises, Markov switching and Lévy jumps are introduced. The threshold conditions to guarantee the extinction and permanence in the mean of the disease with probability one and the existence of unique ergodic stationary distribution for the model are established. Some new techniques to deal with the Markov switching, Lévy jumps, nonlinear incidence and vaccination for the stochastic epidemic models are proposed. Lastly, the numerical simulations not only illustrate the main results given in this paper, but also suggest some interesting open problems.

scholarly journals Comparison of deterministic and stochastic SIRS epidemic model with saturating incidence and immigration

2014 ◽  
Vol 4 (2) ◽  
pp. 101-116 ◽  
Author(s):  
Aadil Lahrouz ◽  
Lahcen Omari ◽  
Adel Settati ◽  
Aziza Belmaâti
Keyword(s):  
Epidemic Model ◽  
Sirs Epidemic Model ◽  
Stochastic Sirs Epidemic Model

scholarly journals Dynamical Behavior of a Stochastic SIRS Epidemic Model

2015 ◽  
Vol 10 (2) ◽  
pp. 56-73 ◽  
Author(s):  
N. T. Hieu ◽  
N. H. Du ◽  
P. Auger ◽  
N. H. Dang
Keyword(s):  
Epidemic Model ◽  
Dynamical Behavior ◽  
Sirs Epidemic Model ◽  
Stochastic Sirs Epidemic Model
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