Local asymptotic stability of an SIS epidemic model with variable population size and a delay

2015 ◽  
Vol 9 ◽  
pp. 3165-3180 ◽  
Author(s):  
Khadija Niri ◽  
Jaafar El Karkri
Keyword(s):  
Asymptotic Stability ◽  
Population Size ◽  
Epidemic Model ◽  
Local Asymptotic Stability ◽  
Sis Epidemic Model ◽  
Variable Population ◽  
Sis Epidemic ◽  
Variable Population Size

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 KICKED EPIDEMIC SIRS MODEL

2012 ◽  
Vol 22 (10) ◽  
pp. 1250251
Author(s):  
F. PALADINI ◽  
I. RENNA ◽  
L. RENNA
Keyword(s):  
Infectious Diseases ◽  
Numerical Simulations ◽  
Population Size ◽  
Discrete Time ◽  
Epidemic Model ◽  
Seasonal Variability ◽  
Sirs Model ◽  
Variable Population ◽  
Variable Population Size

A discrete-time deterministic epidemic model is proposed with the aim of reproducing the behavior observed in the incidence of real infectious diseases, such as oscillations and irregularities. For this purpose, we introduce, in a naïve discrete-time SIRS model, seasonal variability (i) in the loss of immunity and (ii) in the infection probability, modeled by sequences of kicks. Effects of a variable population size (assumed as logistic) are also analyzed. Restrictive assumptions are made on the parameters of the models, in order to guarantee that the transitions are determined by true probabilities, so that comparisons with stochastic discrete-time previsions can be also provided. Numerical simulations show that the characteristics of real infectious diseases can be adequately modeled.

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