%0 Journal Article
%T Stability and Hopf Bifurcation of an SIS Model with Species Logistic Growth and Saturating Infect Rate<br>具有种群Logistic增长及饱和传染率的SIS模型的稳定性和Hopf分支
%A Xu Weijian
%A <br>徐为坚
%J 数学物理学报(A辑)
%D 2008
%I 
%X In this paper, an SIS infective model with species Logistic growth and saturating infective rate is studied. The author discusses the existence and the globally asymptotical stability of the equilibrium, and obtains the threshold value at which disease is eliminated, which is just the basic rebirth number $R_{0}=1$. The author proves that when$R_{0}<1$, the non-disease equilibrium is globally asymptotically stable; when $R_{0}>1$ and $\alpha K\leq 1$, the positive equilibrium is globally asymptotically stable; when $R_{0}>1$ and $ \Delta =0 $, a Hopf bifurcation occurs near the positive equilibrium; when $R_{0}>1$ and $ \Delta <0 $, the system has a unique limit cycle which is stable near the outside of the positive equilibrium.
%K Equilibriumzz
%K Global asymptotic stabilityzz
%K Limit cyclezz
%K Hopf bifurcationzz<br>平衡点
%K 全局渐近稳定
%K 极限环
%K Hopf分支
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=2F03413CE9881C0C98A3EDD154A2878F&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=38B194292C032A66&sid=C2053D4E59904B8A&eid=E04FC1B5BC47587B&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=2&reference_num=14