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Interpreting models of infectious diseases in terms of integral input-to-state stability. (English) Zbl 1458.92074

Summary: 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.

MSC:

92D30 Epidemiology
92C60 Medical epidemiology
93C15 Control/observation systems governed by ordinary differential equations
93D25 Input-output approaches in control theory
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References:

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