一类具有变免疫期的传染病模型的稳定性与分支
Stability and bifurcations in an epidemic model with varying immunity period
摘要：
建立了一个具有分布时滞的传染病模型，用于描述免疫力变化的传染病动力学。结果表明，该模型的解总是正的，并且最多有两个稳定状态：无病和地方病。证明了无病平衡点是局部和全局渐近稳定的。当地方病平衡点存在时，可以使用李雅普诺夫泛函解析地证明其局部和全局稳定性。分岔分析进行使用DDE-BIFTOOL和traceDDE调查不同的动力学制度的模型，使用数值延拓不同的系统参数和不同的积分内核的值。
英文摘要：
An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and endemic. It is proved that the disease-free equilibrium is locally and globally asymptotically stable. When an endemic equilibrium exists, it is possible to analytically prove its local and global stability using Lyapunov functionals. Bifurcation analysis is performed using DDE-BIFTOOL and traceDDE to investigate different dynamical regimes in the model using numerical continuation for different values of system parameters and different integral kernels.
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