scholarly journals Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Haokun Qi ◽  
Lidan Liu ◽  
Xinzhu Meng
Keyword(s):  
Periodic Solution ◽  
Theoretical Analysis ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Nonlinear Incidence Rate ◽  
Sis Epidemic Model ◽  
Stochastic Sis Epidemic Model ◽  
Sis Epidemic

We investigate the dynamics of a nonautonomous stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis. By constructing suitable stochastic Lyapunov functions and using Has’minskii theory, we prove that there exists at least one nontrivial positive periodic solution of the system. Moreover, the sufficient conditions for extinction of the disease are obtained by using the theory of nonautonomous stochastic differential equations. Finally, numerical simulations are utilized to illustrate our theoretical analysis.

scholarly journals Analysis of a Deterministic and a Stochastic SIS Epidemic Model with Double Epidemic Hypothesis and Specific Functional Response

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Mouhcine Naim ◽  
Fouad Lahmidi
Keyword(s):  
Epidemic Model ◽  
Deterministic Model ◽  
Sufficient Condition ◽  
Nonlinear Incidence Rate ◽  
Local Asymptotic Stability ◽  
Sis Epidemic Model ◽  
The Stability ◽  
Stochastic Sis Epidemic Model ◽  
Disease Free ◽  
Sis Epidemic

The purpose of this paper is to investigate the stability of a deterministic and stochastic SIS epidemic model with double epidemic hypothesis and specific nonlinear incidence rate. We prove the local asymptotic stability of the equilibria of the deterministic model. Moreover, by constructing a suitable Lyapunov function, we obtain a sufficient condition for the global stability of the disease-free equilibrium. For the stochastic model, we establish global existence and positivity of the solution. Thereafter, stochastic stability of the disease-free equilibrium in almost sure exponential and pth moment exponential is investigated. Finally, numerical examples are presented.

A stochastic SIS epidemic model with vaccination

2017 ◽  
Vol 486 ◽  
pp. 127-143 ◽  
Author(s):  
Boqiang Cao ◽  
Meijing Shan ◽  
Qimin Zhang ◽  
Weiming Wang
Keyword(s):  
Epidemic Model ◽  
Sis Epidemic Model ◽  
Stochastic Sis Epidemic Model ◽  
Sis Epidemic

Probability analysis of a stochastic SIS epidemic model

2017 ◽  
Vol 17 (06) ◽  
pp. 1750041 ◽  
Author(s):  
Qing Ge ◽  
Zhiming Li ◽  
Zhidong Teng
Keyword(s):  
Positive Integer ◽  
Epidemic Model ◽  
Transition Probabilities ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Sis Epidemic Model ◽  
Number Formula ◽  
Model Transition ◽  
Stochastic Sis Epidemic Model ◽  
Sis Epidemic

In this paper, the probability properties are investigated for a stochastic SIS epidemic model. Transition probabilities of the susceptible process are obtained by using Laplace transform and perturbation variables. According to two cases: basic reproduction number [Formula: see text] and [Formula: see text], the dynamical behaviors in probability of the process are analyzed. It is shown that when [Formula: see text] the disease-free equilibrium is globally asymptotically stable with probability one, and when [Formula: see text] and [Formula: see text] is a positive integer, the endemic equilibrium is globally asymptotically stable with probability one. These results coincide with the corresponding deterministic SIS epidemic model. However, when [Formula: see text] and [Formula: see text] is not a positive integer, there are different properties between the deterministic and stochastic models. Numerical simulations are also performed to validate these results.

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