Dynamic Behavior of the SEIS Model with the Saturating Contact Rate
Zhang Juan，Ma Zhi'en
(School of Sciences, Xi'an Jiaotong University,Xi'an 710049,China)

Abstract: 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 reprodu ction 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.
Keywords: SEIS model;saturating contact rate;dynamic behavior