scholarly journals Stability analysis of SIRS epidemic model on measles disease spreading with vaccination and migration

2021 ◽  
Vol 1872 (1) ◽  
pp. 012033
Author(s):  
I S Kusmawati ◽  
T D Chandra
Keyword(s):  
Stability Analysis ◽  
Epidemic Model ◽  
Sirs Epidemic Model ◽  
Disease Spreading ◽  
And Migration

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
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