一类具有时滞和非线性发生率的SIRS传染病模型稳定性与Hopf分岔分析

研究了一类具有时滞及非线性特性发生率的SIRS传染病模型,首先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稳定性;并以时滞τ作为分岔参数,分析了模型的Hopf分岔行为,运用中心流形定理和规范型理论给出了分岔方向及分岔周期解稳定性的计算公式;最后,数值模拟验证了理论分析结果.

Stability and hopf bifurcation analysis of a delayed sirs epidemic model with nonlinear saturation incidence

An SIRS epidemic model with nonlinear saturation incidence rate and time delay was investigated. By analyzing the corresponding characteristic equations, the local stability of disease-free equilibrium and endemic equilibrium was discussed. The bifurcation property was obtained as the time delay passed through a critical value. Applying the center manifold argument and normal form theory, some local bifurcation results were obtained and the formulas for determining the bifurcation direction and stability of the bifurcated periodic solution were derived. Numerical simulations were presented to illustrate the theoretical analysis.