论文标题
关于基于庞加莱紧凑型的一些爵士流行模型的全球行为
On global behavior of a some SIR epidemic model based on the Poincaré compactification
论文作者
论文摘要
重要的是要研究描述传染病的传播动态的普通微分方程系统的全球行为。在本文中，我们提出了与大多数使用的Lyapunov函数不同的方法。这种方法基于庞加莱的紧凑型。然后，我们将该方法应用于爵士流行模型作为测试案例，并讨论其有效性和该方法的潜在应用。此外，我们还完善了对平衡附近动力学的讨论，得出渐近行为，并提及其与基本繁殖数的关系。
It is important to study the global behavior of solutions to systems of ordinary differential equations describing the transmission dynamics of infectious disease. In this paper, we present a different approach from the Lyapunov function used in most of them. This approach is based on the Poincaré compactification. We then apply the method to a SIR endemic model as a test case, and discuss its effectiveness and the potential applications of this approach. In addition, we refine the discussion of dynamics near the equilibrium, derive the asymptotic behavior, and mention its relation to the basic reproduction number.
