论文标题
输入到州的稳定性和Lyapunov功能，具有显式域的SIR传染病模型
Input-to-state stability and Lyapunov functions with explicit domains for SIR model of infectious diseases
论文作者
论文摘要
本文展示了有关无病平衡和地方性平衡的SIR传染病模型的投入到国家稳定性（ISS）。构建Lyapunov的功能是为了验证两个平衡在新生儿/移民率的扰动方面都具有稳健性，这决定了流行病中最终人口的最终状态。构建和分析是人口空间中的几何和全球。除了建立ISS之外，本文还显示了构造水平集的明确反映轨迹的流程。阐明了Lyapunov功能构建的基本障碍和钥匙。所提出的具有严格负面导数的Lyapunov功能使我们不仅可以建立ISS，还可以摆脱Lasalle的不变性原则的使用和流行的简化假设。
This paper demonstrates input-to-state stability (ISS) of the SIR model of infectious diseases with respect to the disease-free equilibrium and the endemic equilibrium. Lyapunov functions are constructed to verify that both equilibria are individually robust with respect to perturbation of newborn/immigration rate which determines the eventual state of populations in epidemics. The construction and analysis are geometric and global in the space of the populations. In addition to the establishment of ISS, this paper shows how explicitly the constructed level sets reflect the flow of trajectories. Essential obstacles and keys for the construction of Lyapunov functions are elucidated. The proposed Lyapunov functions which have strictly negative derivative allow us to not only establish ISS, but also get rid of the use of LaSalle's invariance principle and popular simplifying assumptions.
