Vol. 8, No. 3, 2020

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A new virus-centric epidemic modeling approach, 1: General theory and machine learning simulation of 2020 SARS Cov 2 (COVID-19) for Belgium, France, Italy, and Spain

Jean Rémond and Yves Rémond

Vol. 8 (2020), No. 3, 233–247

We are trying to test the capacity of a simplified macroscopic virus-centric model to simulate the evolution of the SARS CoV 2 epidemic (COVID 19) at the level of a country or a geographical entity, provided that the evolution of the conditions of its development (behaviors, containment policies) are sufficiently homogeneous on the considered territory. For example, a uniformly deployed lockdown on the territory, or a sufficiently uniform overall crisis management. The virus-centric approach means that we favor to model the population dynamic of the virus rather than the evolution of the human cases. In other words, we model the interactions between the virus and its environment – for instance a specific human population with a specific behavior on a territory, instead of modeling the interactions between individuals. Therefore, our approach assumes that an epidemic can be analyzed as the combination of several elementary epidemics which represent a different part of the population with different behaviors through time. The modeling proposed here is based on the finite superposition of Verhulst equations commonly known as logistic functions and used in dynamics of population. Modelling the lockdown effect at the macroscopic level is therefore possible. Our model has parameters with a clear epidemiological interpretation, therefore the evolution of the epidemic can be discussed and compared among four countries: Belgium, France, Italy, and Spain. Parameter optimization is carried out by a classical machine learning process. We present the number of infected patients with SARS-CoV-2 and a comparison between data from the European Centre for Disease Prevention and Control and the modeling. In a general formulation, the model is applicable to any country with similar epidemic management characteristics. These results show that a simple two epidemics decomposition is sufficient to simulate with accuracy the effect of a lockdown on the evolution of the COVID-19 cases.

SARS-CoV-2, COVID-19, epidemic, modeling, simulation, machine learning, infected cases, logistic function
Mathematical Subject Classification
Primary: 34C60, 68T20, 92-10, 92D25, 92D30
Received: 5 May 2020
Revised: 12 May 2020
Accepted: 16 June 2020
Published: 2 September 2020

Communicated by Francesco dell'Isola
Jean Rémond
Stanwell Consulting
Yves Rémond
ECPM - ICUBE Laboratory
University of Strasbourg / CNRS