Global Stability of SIR Epidemiological Model with Vaccinal Immunity and Bilinear Incidence Rates
XU Wen-xiong, ZHANG Zhong-hua (School of Sciences, Xi'an Jiaotong University, Xi'an710049)
The global stability of SIR epidemiological model with vaccinal immunty and bilinear incidence rates is (studied). The basic reproductive number R_0 is found, which determines the existence of the infective disease. When R_0≤1, there only exists disease free (equilibrium) E_0. While R_01, two equilibriums, the endemic equilibria E~* and the disease free (equilibrium) E_0 exist. By Hurwitz criterion and Liapunov-Lasalle invarient theorem, we have proved the disease free (equilibrium) E_0 is globally asymptotically stable if R_01, while the disease free equilibrium E_0 is unstable and the endemic (equilibrium) E~* is globally asymptotically stable if R_01. Specially, if the basic reproductive number R_0=1, the computer numerical value simulation implies the disease free equilibrium E_0 is possiblly stable.
【CateGory Index】： O29