中文摘要：

利用特征值理论分析了无病平衡点和地方病平衡点的局部渐近稳定性.同时,由于时滞τ的出现,Hopf分岔行为在系统中产生,应用中心流形定理和规范形理论,给出系统的分岔方向及分岔周期解稳定性计算公式.最后,通过数值模拟验证了理论分析结果.

英文摘要：

By analyzing the corresponding characteristic equation, the local stability of disease-free equilibrium and endemic equilibrium is discussed. The bifurcation property is obtained as the delay pass through a critical value. Applying the center manifold and normal form theory, some local bifurcation results are obtained and the formulas for determining the bifurcation direction and stability of the bifurcation periodic solution are derived. Finally, numerical simulations are presented to illustrate the theoretical analysis.