This paper considers an SIRS epidemic model that incorporates constant immigrati on rate, a general population size dependent contact rate and proportional tran sfer rate from the infective class to susceptible class...This paper considers an SIRS epidemic model that incorporates constant immigrati on rate, a general population size dependent contact rate and proportional tran sfer rate from the infective class to susceptible class.A threshold parameter σ is identified. If σ≤1, the disease free equilibrium is globally stab le. If σ>1, a unique endemic equilibrium is locally asymptotically stable. For two important special cases of mass action incidence and standard incidence, global stability of the endemic equilibrium is proved provided the threshold is larger than unity. Some previous results are extended and improved.展开更多
1 Model of Economic Equilibria In the model of a finite economy of pure exchange with n+1 commodities, since only relative prices are essential, the price adjustment can be expressed as a continuous self mapping f of ...1 Model of Economic Equilibria In the model of a finite economy of pure exchange with n+1 commodities, since only relative prices are essential, the price adjustment can be expressed as a continuous self mapping f of S<sup>n</sup>={p∈R<sup>n+1</sup>:p≥O, e<sup>T</sup>p=1}. Thus a fixed point of f is just an equilibrium展开更多
基金Supported by the Science and Technology Foundation of Zhejiang University(1 0 70 0 0 - 54430 1 )
文摘This paper considers an SIRS epidemic model that incorporates constant immigrati on rate, a general population size dependent contact rate and proportional tran sfer rate from the infective class to susceptible class.A threshold parameter σ is identified. If σ≤1, the disease free equilibrium is globally stab le. If σ>1, a unique endemic equilibrium is locally asymptotically stable. For two important special cases of mass action incidence and standard incidence, global stability of the endemic equilibrium is proved provided the threshold is larger than unity. Some previous results are extended and improved.
基金This work is supported in part by the Foundation of Zhongshan University Advanced Research Centre and in part by the National Natural Science Foundation of China.
文摘1 Model of Economic Equilibria In the model of a finite economy of pure exchange with n+1 commodities, since only relative prices are essential, the price adjustment can be expressed as a continuous self mapping f of S<sup>n</sup>={p∈R<sup>n+1</sup>:p≥O, e<sup>T</sup>p=1}. Thus a fixed point of f is just an equilibrium
