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《Chinese Journal of Engineering Mathematics》 2007-06
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The Stability for an Epidemic Model with Vaccinal Immunity and Nonlinear Infectious Rate

LI Da-zhi,GUO Xiao-jun,ZHANG Hui(School of Science,Nantong University,Nantong 226007)  
An epidemic model with vaccinal immunity and nonlinear infectious rate is analyzed in this paper. Derived is a threshold θ which determines the existence of the infectious disease. When θ 1,there only exists disease free equilibrium point E0,which is asymptotically stable;when θ 1,there exist two equilibrium points,the disease free equilibrium point E0 and endemic equilibrium point E+,in which the E0 is unstable. Provided that there is no case of losing immunity or death of diseases,when θ 1,the E0 is globally asymptotically stable,and when θ 1,the E+ is globally asymptotically stable.
【Fund】: 南通大学自然科学基金(06Z008).
【CateGory Index】: O175
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