标题： 伏尔泰拉格子、阿贝尔第一类方程和SIR流行病模型 显示英文标题

标题： The Volterra lattice, Abel's equation of the first kind, and the SIR epidemic models

摘要： 当施加非零常数边界值时，Volterra格子在系统尺寸足够小的情况下，可以构成一个完全可积的哈密顿系统。 这种Volterra格子可以被视为一种已知的SIR疫苗接种模型，它将著名的SIR模型扩展以考虑疫苗接种。 在引入适当的变量变换后，带有疫苗接种的SIR模型会简化为第一类Abel方程，这对应于一个精确微分方程。 精确微分方程的等势曲线是Lambert曲线。 因此，通过使用Lambert W函数，可以隐式地提供带有疫苗接种的SIR模型或具有常数边界值的Volterra格子的初值问题的一般解。 显示英文摘要

摘要： The Volterra lattice, when imposing non-zero constant boundary values, admits the structure of a completely integrable Hamiltonian system if the system size is sufficiently small. Such a Volterra lattice can be regarded as an epidemic model known as the SIR model with vaccination, which extends the celebrated SIR model to account for vaccination. Upon the introduction of an appropriate variable transformation, the SIR model with vaccination reduces to an Abel equation of the first kind, which corresponds to an exact differential equation. The equipotential curve of the exact differential equation is the Lambert curve. Thus, the general solution to the initial value problem of the SIR model with vaccination, or the Volterra lattice with constant boundary values, is implicitly provided by using the Lambert W function.