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.