一类具有非线性发生率的时滞传染病模型的全局稳定性

充分考虑人口统计效应、疾病的潜伏期与传播规律的复杂性，研究了一类具有非线性发生率的时滞SIRS传染病模型的动力学行为.通过分析对应的线性化近似系统的特征方程，证明了无病平衡点的局部稳定性.利用Lyapunov-LaSalle不变集原理，当基本再生数R₀<1时，证明了无病平衡点是全局渐近稳定的；当R₀>1时，得到了地方病平衡点全局渐近稳定的充分条件.所得结论可为人们有效预防和控制传染病传播提供一定的理论依据.

Global Stability of a Class of Delayed Epidemic Models With Nonlinear Incidence Rates

In view of the demographic effects, the latent period and the complexity of disease spread, the dynamic behavior of a class of delayed SIRS epidemic models with nonlinear incidence rates was investigated. The characteristic equation of the corresponding linearized approximation system was analyzed to prove the local stability of the disease-free equilibrium. By means of the Lyapunov-LaSalle invariant set principle, it was proved that the disease-free equilibrium was globally asymptotically stable when the basic reproduction number was less than 1; and the sufficient conditions were obtained for the global asymptotic stability of the endemic equilibrium when the basic reproduction number was greater than 1. Consequently, the conclusions provide a theoretical reference for the effective prevention and control of the spread of communicable diseases.