This paper aims to develop a system-theoretic approach to ordinary differential equations which deterministically describe dynamics of prevalence of epidemics. The equations are treated as interconnections in which component systems are connected by signals. The notions of integral input-to-state stability (iISS) and input-to-state stability (ISS) have been effective in addressing nonlinearities globally without domain restrictions in analysis and design of control systems. They provide useful tools of module-based methods integrating characteristics of component systems. This paper expresses fundamental properties of models of infectious diseases and vaccination through the language of iISS and ISS of components and whole systems. The systematic treatment is expected to facilitate development of effective schemes of controlling the disease spread via non-conventional Lyapunov functions.

本文旨在为确定性地描述流行病流行动态的常微分方程建立一种系统理论的方法。这些方程式被视为互连，其中组件系统通过信号连接。积分输入状态稳定性（iISS）和输入状态稳定性（ISS）的概念已在全球范围内有效解决非线性问题，而在控制系统的分析和设计中没有领域限制。它们提供了集成组件系统特征的基于模块的方法的有用工具。本文通过组成部分和整个系统的iISS和ISS语言表达了传染病和疫苗接种模型的基本特性。