Asymptotic profiles of a diffusive SIRS epidemic model with standard incidence mechanism and a logistic source

2022 ◽  
Vol 73 (1) ◽  
Author(s):  
Yifei Pan ◽  
Siyao Zhu ◽  
Jinliang Wang
Keyword(s):  
Epidemic Model ◽  
Logistic Source ◽  
Sirs Epidemic Model

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

scholarly journals A Node-Based SIRS Epidemic Model with Infective Media on Complex Networks

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Leyi Zheng ◽  
Longkun Tang
Keyword(s):  
Epidemic Model ◽  
Small World ◽  
Spreading Rate ◽  
Node Degree ◽  
Strong Positive Correlation ◽  
Globally Asymptotically Stable ◽  
Sirs Epidemic Model ◽  
Theoretical Investigations ◽  
Fully Connected ◽  
The Impact

We focus on the node-based epidemic modeling for networks, introduce the propagation medium, and propose a node-based Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model with infective media. Theoretical investigations show that the endemic equilibrium is globally asymptotically stable. Numerical examples of three typical network structures also verify the theoretical results. Furthermore, comparison between network node degree and its infected percents implies that there is a strong positive correlation between both; namely, the node with bigger degree is infected with more percents. Finally, we discuss the impact of the epidemic spreading rate of media as well as the effective recovered rate on the network average infected state. Theoretical and numerical results show that (1) network average infected percents go up (down) with the increase of the infected rate of media (the effective recovered rate); (2) the infected rate of media has almost no influence on network average infected percents for the fully connected network and NW small-world network; (3) network average infected percents decrease exponentially with the increase of the effective recovered rate, implying that the percents can be controlled at low level by an appropriate large effective recovered rate.

Sign in / Sign up

Export Citation Format

Share Document