ArticleIEEE control systems letters2022
The Basic Reproduction Number as a Loop Gain Matrix.
Article in IEEE control systems letters, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
The COVID-19 pandemic and the disordered reactions of most governments made the importance of mathematical modelling and model-based predictions evident, even outside the scientific community. The basic reproduction number [Formula: see text] quickly entered the common jargon, as a concise but effective tool to communicate the spreading power of a disease and estimate, at least roughly, the possible outcomes of the epidemic. However, while [Formula: see text] is easily defined for simple models, its proper definition is more subtle for larger, state-of-the-art models. Here we show that it is nothing else than the spectral radius of the gain matrix of a linear system, and that this matrix generalizes [Formula: see text] in the computation of the vector-valued final epidemic size and epidemic threshold, in a large class of finite-dimensional SIR-like models.
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