具有饱和接触率的SEIS模型的动力学性质

研究了具有饱和接触率的SEIS模型的动力学性质，得到了决定疾病绝灭或持续生存的基本再生数。对于不会因病致死的传染病，证明了地方病平衡点只要存在就是全局渐近稳定的。研究结果表明：具有饱和接触率的SEIS模型的基本再生数与具有线性或常数接触率模型的基本再生数相比有所下降。

Dynamic Behavior of the SEIS Model with the Saturating Contact Rate

Dynamical behaviors of the SEIS model for the transmission an infectious desease that spreads in a population throught direct contact of hosts is studied. The contact number of individuals contacts in unit time tends to saturate, that is, the number of contacts grow less rapidly as population size increases. The basic reproduction number which determines the outcome of the disease is identified; if the basic reproduction number is not greater than 1, the infected fraction of the population disappears, so the disease dies out, If the basic reproduction number is greater 1, the infected fraction persists, so the disease remains the endemic. Especially when the death rate due to disease is very small and can be negligible, global stability of the endemic equilibrium is proved. The results show that the basic reproduction number of the SEIS model with the saturating contact rate is less than that of the SEIS model with the linear or constant contact rate.