scholarly journals Permanence of a delayed SIR epidemic model with density dependent birth rate

2007 ◽  
Vol 201 (2) ◽  
pp. 389-394 ◽  
Author(s):  
Mei Song ◽  
Wanbiao Ma ◽  
Yasuhiro Takeuchi
Keyword(s):  
Epidemic Model ◽  
Birth Rate ◽  
Sir Epidemic Model ◽  
Density Dependent ◽  
Sir Epidemic

scholarly journals Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Li Yingke ◽  
Chen Liang ◽  
Wang Kai
Keyword(s):  
Differential Equations ◽  
Epidemic Model ◽  
Birth Rate ◽  
Distributed Delay ◽  
Threshold Value ◽  
Sir Epidemic Model ◽  
Classical Analysis ◽  
Density Dependent ◽  
Analysis Techniques ◽  
Sir Epidemic

Based on some well-known SIR models, a revised nonautonomous SIR epidemic model with distributed delay and density-dependent birth rate was considered. Applying some classical analysis techniques for ordinary differential equations and the method proposed by Wang (2002), the threshold value for the permanence and extinction of the model was obtained.

scholarly journals On the Integrability of the SIR Epidemic Model with Vital Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Ding Chen
Keyword(s):  
Epidemic Model ◽  
Birth Rate ◽  
Sir Model ◽  
Point Of View ◽  
Algebraic Surfaces ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Invariant Algebraic Surfaces ◽  
Invariant Algebraic Surface

In this paper, we study the SIR epidemic model with vital dynamics Ṡ=−βSI+μN−S,İ=βSI−γ+μI,Ṙ=γI−μR, from the point of view of integrability. In the case of the death/birth rate μ=0, the SIR model is integrable, and we provide its general solutions by implicit functions, two Lax formulations and infinitely many Hamilton-Poisson realizations. In the case of μ≠0, we prove that the SIR model has no polynomial or proper rational first integrals by studying the invariant algebraic surfaces. Moreover, although the SIR model with μ≠0 is not integrable and we cannot get its exact solution, based on the existence of an invariant algebraic surface, we give the global dynamics of the SIR model with μ≠0.

Analisis Titik Kesetimbangan Dan Kestabilan Penyebaran Penyakit Malaria di Distrik Manokwari Barat Berdasarkan Model Epidemik SIR

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Fandy Fandy ◽  
Andi Fajeriani Wyrasti ◽  
Tri Widjajanti
Keyword(s):  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Endemic Diseases ◽  
Sir Epidemic

<em>Stability and equilibrium of malaria&rsquo;s epidemics in Manokwari Barat district based on SIR epidemic model will be discussed in this paper. The SIR epidemic model can be applied to make a model of endemic diseases like malaria. Based on this research, there are 2 types of the equilibrium of malaria&rsquo;s epidemics in Manokwari Barat District, endemic and non endemic point.</em>

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