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Stability in Two SIQ Model with and without Vaccination

  • Chahrazed, LAID
The present paper presents a study of a SIQR model with and without vaccination. The first model is a model nonlinear epidemic which analyzes the spread and stability of the model epidemic. A population of size N (t) at time t, is divided into for sub classes, the susceptible to disease, and infectious members, members quarantine with the possibility of infection through temporary immunity, and who were removed from the possibility of infection respectively. In comparison with the model 1, we introduced the vaccination and we study equilibrium and stability of the both models, we define the basic reproduction number of the infection R₀ then if R₀ ≤ 1 the disease-free equilibrium E₀ is globally asymptotically stable, and if Ro> 1 system has a unique non-trivial equilibrium which is globally asymptotically stable. By introducing vaccination in the second model became Rv, or to the disease-free equilibrium is globally asymptotically stable, if Rv ≤ 1, and, if Rv> 1, system has a unique non-trivial equilibrium which is globally asymptotically stable. The study of the two models with and without vaccination we used the references if below: Different variations of the epidemic model have been studied in [1,2,4,6,11,12,16,19,20,21,29]. The stochastic epidemic model in [3,7,14,15], and the stability of different models in [8,9,13,22,23,24,28,30,31]. The solutions for different delay differentials equations in [5,10,18,25,26,27].
Select Volume / Issue:
Year:
2017
Type of Publication:
Article
Keywords:
Basic Reproduction Number; Endemic Equilibrium; Global Asymptotic Stability; Epidemic Model; Lyapunov Functional; Temporary Immunity; Vaccination
Journal:
IJASM
Volume:
4
Number:
1
Pages:
8-11
Month:
January
ISSN:
2394-2894
Hits: 1132

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