Threshold dynamics of a stochastic SIS epidemic model with nonlinear incidence rate

2019 ◽  
Vol 526 ◽  
pp. 120946 ◽  
Author(s):  
Qun Liu ◽  
Daqing Jiang ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Threshold Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sis Epidemic Model ◽  
Stochastic Sis Epidemic Model ◽  
Sis Epidemic

A SIS Epidemic Model with Eventual Impulsive Effects

2013 ◽  
Vol 393 ◽  
pp. 666-674
Author(s):  
Manuel de La Sen ◽  
A. Ibeas ◽  
S. Alonso-Quesada
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Total Population ◽  
Disease Model ◽  
Impulsive Effects ◽  
Time Varying ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sis Epidemic Model ◽  
Sis Epidemic

This paper studies a time-varyingSIS(i.e.containing susceptible and infected populations) propagation disease model exhibiting a nonlinear incidence rate and impulsive eventual culling of both populations so that the individuals recover with no immunity to the disease. The nonlinear incidence rate consists of two time-varying additive terms proportional to the susceptible and infected populations normalized to the total population.

scholarly journals Extinction and Ergodic Property of Stochastic SIS Epidemic Model with Nonlinear Incidence Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Qixing Han ◽  
Daqing Jiang ◽  
Chengjun Yuan
Keyword(s):  
Incidence Rate ◽  
Nonnegative Solution ◽  
Ergodic Property ◽  
Nonlinear Incidence Rate ◽  
Sis Model ◽  
Nonlinear Incidence ◽  
Sis Epidemic Model ◽  
Stochastic Sis Epidemic Model ◽  
Sis Epidemic ◽  
Stochastic Sis Model

We investigate a stochastic SIS model with nonlinear incidence rate. We show that there exists a unique nonnegative solution to the system, and condition for the infectious individualsI(t)to be extinct is given. Moreover, we prove that the system has ergodic property. Finally, computer simulations are carried out to verify our results.

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.

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