A Stochastic Switched Epidemic Model with Two Epidemic Diseases

In this paper, we study a stochastic epidemic model with double epidemics which includes white noise and telegraph noise modeled by Markovian switching. Sufficient conditions for the extinction and persistence of the diseases are established. In the end, some numerical simulations are presented to demonstrate our analytical results.

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Dynamics of a stochastic rabies epidemic model with markovian switching

International Journal of Biomathematics ◽

10.1142/s1793524521500327 ◽

2021 ◽

pp. 2150032

Author(s):

Hao Peng ◽

Xinhong Zhang ◽

Daqing Jiang

Keyword(s):

Lyapunov Function ◽

White Noise ◽

Numerical Simulations ◽

Positive Solution ◽

Epidemic Model ◽

Sufficient Conditions ◽

Sufficient Condition ◽

Telegraph Noise ◽

Global Positive Solution ◽

Theoretical Results

In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for the extinction of diseases. Finally, numerical simulations are introduced to illustrate our theoretical results.

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Study on a susceptible–infected–vaccinated model with delay and proportional vaccination

International Journal of Biomathematics ◽

10.1142/s1793524518501024 ◽

2018 ◽

Vol 11 (08) ◽

pp. 1850102 ◽

Cited By ~ 1

Author(s):

Shuqi Gan ◽

Fengying Wei

Keyword(s):

Positive Solution ◽

Epidemic Model ◽

Sufficient Conditions ◽

Sufficient Condition ◽

Stochastic Epidemic ◽

Persistence In The Mean ◽

Global Positive Solution ◽

The Mean ◽

Stochastic Epidemic Model

A susceptible–infected–vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and global positive solution with probability one when constructing a proper [Formula: see text]-function therewith. Then a sufficient condition that guarantees the disappearances of diseases is derived when the indicator [Formula: see text]. Further, if [Formula: see text], then we obtain that the solution is weakly permanent with probability one. We also derived the sufficient conditions of the persistence in the mean for the susceptible and infected when another indicator [Formula: see text].

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Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine

Journal of Applied Mathematics ◽

10.1155/2018/1291402 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Driss Kiouach ◽

Lahcen Boulaasair

Keyword(s):

Numerical Simulations ◽

Stationary Distribution ◽

Epidemic Model ◽

Critical Condition ◽

Dynamic Behaviour ◽

Sufficient Conditions ◽

Analytical Results ◽

The Mean

We consider a stochastic SIVR (susceptible-infected-vaccinated-recovered) epidemic model with imperfect vaccine. First, we obtain critical condition under which the disease is persistent in the mean. Second, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Third, we study the extinction of the disease. Finally, numerical simulations are given to support the analytical results.

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A hepatitis stochastic epidemic model with acute and chronic stages

Advances in Difference Equations ◽

10.1186/s13662-021-03335-7 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Amir Khan ◽

Ghulam Hussain ◽

Abdullahi Yusuf ◽

Auwalu Hamisu Usman ◽

Usa Wannasingha Humphries

Keyword(s):

Epidemic Model ◽

Transmission Rate ◽

Sufficient Conditions ◽

Environmental Fluctuation ◽

Stochastic Perturbations ◽

Proposed Model ◽

Stochastic Epidemic ◽

Persistence In The Mean ◽

Global Positive Solution ◽

Stochastic Epidemic Model

AbstractThe article is based on the study of hepatitis transmission dynamics using a stochastic epidemic model. We discuss the stochastic perturbations of our proposed model by considering the effect of environmental fluctuation and distribute the transmission rate in the form of white noise. Taking into account the Lyapunov function theory, the uniqueness and existence of the global positive solution are proven. Some sufficient conditions for the extinction and persistence in the mean are established. The numerical simulations are given to verify the main theoretical findings.

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Dynamics analysis and numerical simulations of a delayed stochastic epidemic model subject to a general response function

Computational and Applied Mathematics ◽

10.1007/s40314-019-0857-x ◽

2019 ◽

Vol 38 (2) ◽

Cited By ~ 13

Author(s):

Fei Li ◽

Shengqiang Zhang ◽

Xinzhu Meng

Keyword(s):

Numerical Simulations ◽

Response Function ◽

Epidemic Model ◽

Dynamics Analysis ◽

Stochastic Epidemic ◽

Stochastic Epidemic Model ◽

General Response ◽

Model Subject

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Stochastic epidemic dynamics based on the association between susceptible and recovered individuals

International Journal of Biomathematics ◽

10.1142/s1793524520500850 ◽

2020 ◽

pp. 2050085

Author(s):

Luyao Xin ◽

Yingxin Guo ◽

Quanxin Zhu

Keyword(s):

Mathematical Model ◽

White Noise ◽

Numerical Simulations ◽

Sufficient Conditions ◽

Deterministic Case ◽

Epidemic Dynamics ◽

Stochastic Epidemic ◽

The Stability ◽

Permanence In Mean ◽

Theoretical Results

In this paper, we propose a new mathematical model based on the association between susceptible and recovered individual. Then, we study the stability of this model with the deterministic case and obtain the conditions for the extinction of diseases. Moreover, in view of the association between susceptible and recovered individual perturbed by white noise, we also give sufficient conditions for the extinction and the permanence in mean of disease with the white noise. Finally, we have numerical simulations to demonstrate the correctness of obtained theoretical results.

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