Interpreting models of infectious diseases in terms of integral input-to-state stability

TL;DR

This paper applies integral input-to-state stability (iISS) and input-to-state stability (ISS) concepts to infectious disease models, aiming to enhance understanding and control strategies for epidemics using a module-based analysis framework.

Contribution

It introduces a systematic approach to analyze infectious disease dynamics using iISS and ISS, bridging control theory with epidemiological modeling.

Findings

Expresses epidemic properties through iISS and ISS frameworks

Facilitates development of control schemes for disease spread

Provides a unified stability analysis method for epidemiological models

Abstract

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. In particular, they provide useful tools of module-based methods integrating characteristics of components. This paper applies the framework of module-based analysis to ordinary differential equations which deterministically describe dynamics of prevalence and the duration of epidemics. The objective is to express fundamental properties of models of infectious diseases and vaccination through the language of iISS and ISS. The systematic treatment is expected to facilitate development of effective schemes of controlling the spread of diseases via non-conventional Lyapunov functions.