Interpreting models of infectious diseases in terms of integral input-to-state stability
- PDF / 680,778 Bytes
- 21 Pages / 439.37 x 666.142 pts Page_size
- 1 Downloads / 172 Views
Interpreting models of infectious diseases in terms of integral input-to-state stability Hiroshi Ito1 Received: 2 May 2020 / Accepted: 13 November 2020 © The Author(s), under exclusive licence to Springer-Verlag London Ltd. part of Springer Nature 2020
Abstract 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. Keywords Epidemic models · Integral input-to-state stability · Lyapunov functions · Positive nonlinear network · Small-gain theorem
1 Introduction For many decades, mathematical models of infectious diseases have been recognized as useful tools for public health decision-making during epidemics [2,18,27,28]. Detailed models help predict the future course of outbreak, while simple models allow one to understand mechanisms whose interpretations can lead to ideas of control strategies, such as vaccination, isolation, regulation and digital contact tracing or culling, which slow or ultimately eradicate the infection from the population. The objective of this paper is to facilitate the development of the latter. This paper does not report any novel
The work is supported in part by JSPS KAKENHI Grant Number JP20K04536.
B 1
Hiroshi Ito [email protected] Department of Intelligent and Control Systems, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka 820-8502, Japan
123
Mathematics of Control, Signals, and Systems
behavior of disease transmission. Instead, this paper is devoted to a system and signal interpretation of behavior of classical and simple models of infectious diseases in the language of integral input-to-state stability (iISS) and input-to-state stability (ISS). It aims to take a first step toward development of an iISS/ISS-theoretic foundation for control design to combat infectious diseases. This paper reports that popular models share essentially the same qualitative behavior which can be analyzed and explained systematically via the same tools of iISS/ISS. The notions of iISS and ISS have been accepted widely as mathematical tools to deal with and utilize nonlinearities effectively in the area of control [43–45]. The notions offer a systematic framework of module-based design of control systems. Once a system or a network is divided into “stable” c
Data Loading...
