Strict Smooth Lyapunov Functions and Vaccination Control of the SIR Model Certified by ISS

• 成果类型: Article
• 署名作者: Ito, Hiroshi
• 署名单位: Kyushu Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3161395
• 发表日期: 2022
• 页码: 4514-4528
• 关键词: Lyapunov methods; statistics; sociology; asymptotic stability; mathematical models; Robustness; Analytical models; Control Lyapunov functions; epidemic model; global analysis; input-to-state stability (ISS); strict Lyapunov functions; vaccination control

摘要

This article addresses analysis and control of the SIR model of infectious diseases in the framework of input-to-state stability (ISS) with respect to the net flow of susceptible individuals into a region in both disease-free and epidemic situations. The key development is the construction of a continuously differentiable strict Lyapunov function. First, this article clarifies that a continuously differentiable Lyapunov function whose derivative is nonpositive can deduce asymptotic stability on the whole state space. Second, it is demonstrated that a new idea of rendering the derivative strictly negative allows one to detect a margin proving ISS of the SIR model. The accomplishment is based on the pursuit of a Lyapunov function that is not entirely separable into components. It contrasts with previously studied and popular Lyapunov functions that are proven to be incapable of assessing robustness properties such as ISS. Third, two types of feedback control laws are proposed for mass vaccination of immigrants and inhabitants by making use of the strict Lyapunov functions. One type modifies the other type by focusing on the reduction of peaks of the infected population within the ISS guarantees.