%0 Journal Article
%T Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent
%A Tiantian Li
%A Yakui Xue
%J Applied Mathematics
%P 109-117
%@ 2152-7393
%D 2013
%I Scientific Research Publishing
%R 10.4236/am.2013.410A2011
%X <p>
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	<a name=\"OLE_LINK37\"></a><a name=\"OLE_LINK36\"></a><span>In this paper,</span><span> </span><span>we study a kind of the delayed SEIQR infectious disease model with</span><span> </span><span>the quarantine and latent, and get the threshold value which determines the global</span><span> </span><span>dynamics and the outcome of the disease. The model has a disease-free equilibrium</span><span> </span><span>which is unstable when the basic reproduction number is greater than unity.</span><span> </span><span>At the</span><span> </span><span>same time, it has a unique endemic equilibrium when the basic reproduction number</span><span> </span><span>is greater than unity. According to the mathematical dynamics analysis, we show</span><span> </span><span>that disease-free equilibrium and endemic equilibrium are </span><span>locally</span><span> </span><span>asymptotically stable</span><span> by</span><span> </span><span>using Hurwitz criterion and they are globally asymptotically stable by using suitable</span><span> </span><span>Lyapunov functions for any <img alt=\"\" src=\"Edit_284ee28f-a80d-4a2a-ac8f-72b348be4d8e.png\" /></span><span> </span><span><span></span><span></span><span>Besides,</span><span> </span><span>the SEIQR model with nonlinear incidence rate is studied</span><span>, a</span><span>nd the</span><span> <img alt=\"\" src=\"Edit_87230881-e679-44b3-9cfa-accae72773ee.png\" /></span><span> </span><span>that the basic reproduction number is </span><span>a </span><span>unity can be</span><span> found ou</span><span>t. Finally, numerical simulations are performed to illustrate and verify the</span><span> </span><span>conclusions that will be use<span>ful for us to control the spread of infectious diseases.</span></span><span> </span><span>Meanwhile, the</span><span> <img alt=\"\" src=\"Edit_87690537-83a9-4dc1-a0bc-f7297e666e78.png\" /></span><span> </span><span>will effect changing trends of</span><span> <img alt=\"\" src=\"Edit_8de48f15-bf27-42a6-8a3d-72b187d46c78.png\" /><img alt=\"\" src=\"Edit_91f47ffe-e8db-40cf-b541-6e08b379ce30.png\" /></span><span> </span><span>in system (1),</span><span> </span><span>which is obvious in simulations. Here, we take</span><span> <img alt=\"\" src=\"Edit_c2f2d155-7e4a-40f2-bea4-2743cda6d27a.png\" /></span><span> </span><span>as an example to explain that.</span></span> 
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%K SEIQR Model
%K Lyapunov Function
%K Delay
%K Global Stability
%K Nonlinear Incidence Rate
%K Simulations
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=38059