scholarly journals Stability results on age-structured SIS epidemic model with coupling impulsive effect

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Helong Liu ◽  
Houbao Xu ◽  
Jingyuan Yu ◽  
Guangtian Zhu
Keyword(s):  
Blood Transfusion ◽  
Epidemic Model ◽  
Impulsive Effect ◽  
Asymptotically Stable ◽  
Transmission Rates ◽  
Sis Epidemic Model ◽  
Age Structured ◽  
Stability Results ◽  
Time Lead ◽  
Sis Epidemic

We develop an age-structured epidemic model for malaria with impulsive effect, and consider the effect of blood transfusion and infected-vector transmission. Transmission rates depend on age. We derive the condition in which eradication solution is locally asymptotically stable. The condition shows that large enough pulse reducing proportion and relatively small interpulse time lead to the eradication of the diseases.

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.

scholarly journals Stability Results for an Age-Structured SIS Epidemic Model with Vector Population

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
He-Long Liu ◽  
Jing-Yuan Yu ◽  
Guang-Tian Zhu
Keyword(s):  
Fixed Point ◽  
Epidemic Model ◽  
Fixed Point Problem ◽  
Host Population ◽  
Point Problem ◽  
Sis Epidemic Model ◽  
Vector Population ◽  
Point Operator ◽  
Age Structured ◽  
Sis Epidemic

We formulate an age-structured SIS epidemic model with periodic parameters, which includes host population and vector population. The host population is described by two partial differential equations, and the vector population is described by a single ordinary differential equation. The existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on locally integrable periodic functions. We obtain that if the spectral radius of the Fréchet derivative of the fixed point operator at zero is greater than one, there exists a unique endemic periodic solution, and we investigate the global attractiveness of disease-free steady state of the normalized system.

Dynamical analysis of the SIS epidemic model in cluster events

2021 ◽  
Author(s):  
Dun Han ◽  
Junjie Wei ◽  
Haidong Xu ◽  
Dandan Li
Keyword(s):  
Epidemic Model ◽  
Dynamical Analysis ◽  
Sis Epidemic Model ◽  
Sis Epidemic

scholarly journals Endemic Behaviour of SIS Epidemics with General Infectious Period Distributions

2014 ◽  
Vol 46 (01) ◽  
pp. 241-255 ◽  
Author(s):  
Peter Neal
Keyword(s):  
Epidemic Model ◽  
Branching Process ◽  
Endemic Equilibrium ◽  
Infectious Period ◽  
Sis Epidemic Model ◽  
Branching Process With Immigration ◽  
Sis Epidemic ◽  
Sis Epidemics ◽  
Surprising Observation

We study the endemic behaviour of a homogeneously mixing SIS epidemic in a population of size N with a general infectious period, Q, by introducing a novel subcritical branching process with immigration approximation. This provides a simple but useful approximation of the quasistationary distribution of the SIS epidemic for finite N and the asymptotic Gaussian limit for the endemic equilibrium as N → ∞. A surprising observation is that the quasistationary distribution of the SIS epidemic model depends on Q only through

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