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Open AccessArticle

A Brief Theory of Epidemic Kinetics

Grenoble Institute of Technology and Laboratoire de Glaciologie et de Geophysique de l’Environnement, CNRS, Grenoble University (Retired), 38410 St Martin d’Uriage, France
Biology 2020, 9(6), 134; https://doi.org/10.3390/biology9060134
Received: 11 April 2020 / Revised: 7 June 2020 / Accepted: 17 June 2020 / Published: 22 June 2020
(This article belongs to the Special Issue Theories and Models on COVID-19 Epidemics)
In the context of the COVID-19 epidemic, and on the basis of the Theory of Dynamical Systems, we propose a simple theoretical approach for the expansion of contagious diseases, with a particular focus on viral respiratory tracts. The infection develops through contacts between contagious and exposed people, with a rate proportional to the number of contagious and of non-immune individuals, to contact duration and turnover, inversely proportional to the efficiency of protection measures, and balanced by the average individual recovery response. The obvious initial exponential increase is readily hindered by the growing recovery rate, and also by the size reduction of the exposed population. The system converges towards a stable attractor whose value is expressed in terms of the “reproductive rate” R0, depending on contamination and recovery factors. Various properties of the attractor are examined, and particularly its relations with R0. Decreasing this ratio below a critical value leads to a tipping threshold beyond which the epidemic is over. By contrast, significant values of the above ratio may bring the system through a bifurcating hierarchy of stable cycles up to a chaotic behaviour. View Full-Text
Keywords: epidemic; COVID-19; contamination kinetics; herd immunity; dynamical systems; reproductive rate; critical state; attractor; stable cycle; chaos epidemic; COVID-19; contamination kinetics; herd immunity; dynamical systems; reproductive rate; critical state; attractor; stable cycle; chaos
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Louchet, F. A Brief Theory of Epidemic Kinetics. Biology 2020, 9, 134.

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