中文摘要：

利用稳定性理论和齐次向量场的性质对一类传染病模型的一般情形进行研究，通过对R2中相应系统的平衡点的存在性和稳定性的分析，得出该类传染病持续生存和最终消亡的阈值，而且它与治愈者的死亡率以及治愈者向易感者的转化率无关．

英文摘要：

In this paper,we propose an epidemiological model in a normal situation. This model is established in the form of differential equations. The dynamical behavior of the model is studied by using the method of homogeneous vector fields. By analyzing the existence and stability of the system＇s equilibrium point, we get the threshold of disease spread and death. The results do not relate with the ratio of death of recovery and ratio of transitions of recovery to susceptible persons.