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.

scholarly journals Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Lei Wang ◽  
Zhidong Teng ◽  
Tingting Tang ◽  
Zhiming Li
Keyword(s):  
Disease Transmission ◽  
Threshold Dynamics ◽  
Sufficient Condition ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Dynamical Behaviors ◽  
Threshold Conditions ◽  
The Mean ◽  
Stochastic Sirs Epidemic Model ◽  
Theoretical Results

In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed.

Hopf bifurcation of a delay SIRS epidemic model with novel nonlinear incidence: Application to scarlet fever

2018 ◽  
Vol 11 (07) ◽  
pp. 1850091 ◽  
Author(s):  
Yong Li ◽  
Xianning Liu ◽  
Lianwen Wang ◽  
Xingan Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Epidemic Model ◽  
Scarlet Fever ◽  
Reproduction Number ◽  
Control Strategies ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Intervention Measures ◽  
Theoretical Results

An [Formula: see text] epidemic model incorporating incubation time delay and novel nonlinear incidence is proposed and analyzed to seek for the control strategies of scarlet fever, where the contact rate which can reflect the regular behavior and habit changes of children is non-monotonic with respect to the number of susceptible. The model without delay may exhibit backward bifurcation and bistable states even though the basic reproduction number is less than unit. Furthermore, we derive the conditions for occurrence of Hopf bifurcation when the time delay is considered as a bifurcation parameter. The data of scarlet fever of China are simulated to verify our theoretical results. In the end, several effective preventive and intervention measures of scarlet fever are found out.

scholarly journals On the threshold dynamics of the stochastic SIRS epidemic model using adequate stopping times

2020 ◽  
Vol 25 (5) ◽  
pp. 1985-1997
Author(s):  
Adel Settati ◽  
◽  
Aadil Lahrouz ◽  
Mustapha El Jarroudi ◽  
Mohamed El Fatini ◽  
...  
Keyword(s):  
Epidemic Model ◽  
Stopping Times ◽  
Threshold Dynamics ◽  
Sirs Epidemic Model ◽  
Stochastic Sirs Epidemic Model

scholarly journals Dynamics of a Stochastic SIRS Epidemic Model with Regime Switching and Specific Functional Response

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Amine EL Koufi ◽  
Abdelkrim Bennar ◽  
Noura Yousfi
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Regime Switching ◽  
Unique Positive Solution ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Incident Rate ◽  
Stochastic Sirs Epidemic Model

The purpose of this work is to investigate the dynamic behaviors of the SIRS epidemic model with nonlinear incident rate under regime switching. We establish the existence of a unique positive solution of our system. Furthermore, we obtain the conditions for the extinction of diseases, and we show the existence of the stationary distribution for our stochastic SIRS model under regime switching. Numerical simulations are employed to illustrate our theoretical analysis.

Dynamics of a stochastic SIRS epidemic model with standard incidence under regime switching

2021 ◽  
pp. 2150074
Author(s):  
Jiang Xu ◽  
Yinong Wang ◽  
Zhongwei Cao
Keyword(s):  
Lyapunov Function ◽  
Stochastic System ◽  
Epidemic Model ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Sirs Epidemic Model ◽  
Persistence In The Mean ◽  
The Mean ◽  
Stochastic Sirs Epidemic Model ◽  
Stochastic Lyapunov Function

The goal of this paper is to introduce and initiate a study of a stochastic SIRS epidemic model with standard incidence which is perturbed by both white and telegraph noises. We first show persistence in the mean and then establish the sufficient conditions for extinction of the disease. Moreover, in the case of persistence, we obtain sufficient conditions for the existence of positive recurrence of the solutions by means of structuring suitable stochastic Lyapunov function with regime switching. Meanwhile, the threshold between persistence in the mean and extinction of the stochastic system is also obtained. Finally, we test our theory conclusion by simulations.

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