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A Brief Theory of Epidemic Kinetics
Version 1
: Received: 14 April 2020 / Approved: 16 April 2020 / Online: 16 April 2020 (08:20:50 CEST)
A peer-reviewed article of this Preprint also exists.
Louchet, F. A Brief Theory of Epidemic Kinetics. Biology 2020, 9, 134. Louchet, F. A Brief Theory of Epidemic Kinetics. Biology 2020, 9, 134.
Abstract
In the context of the COVID-19 epidemic, and on the basis of the Theory of Dynamical Systems, we propose a simple model 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 contact duration and turnover, inversely proportional to the efficiency of protection measures, and balanced by the average immunological response. The obvious initial exponential increase is readily hindered by the size reduction of the exposed population. The system converges towards a stable attractor whose value is expressed in terms of the ratio C/D of contamination vs decay factors. Decreasing this ratio below a critical value leads to a tipping point beyond which the epidemic is over. By contrast, significant values of C/D may bring the system through a bifurcating hierarchy of stable cycles up to a chaotic behaviour.
Keywords
epidemic; COVID-19; contamination kinetics; immunological response; dynamical systems; reproduction rate; critical state; attractor; stable cycle; chaos
Subject
Medicine and Pharmacology, Epidemiology and Infectious Diseases
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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