  With the unfolding of the COVID-19 pandemic, mathematical modeling of
epidemics has been perceived and used as a central element in understanding,
predicting, and governing the pandemic event. However, soon it became clear
that long term predictions were extremely challenging to address. Moreover, it
is still unclear which metric shall be used for a global description of the
evolution of the outbreaks. Yet a robust modeling of pandemic dynamics and a
consistent choice of the transmission metric is crucial for an in-depth
understanding of the macroscopic phenomenology and better-informed mitigation
strategies. In this study, we propose a Markovian stochastic framework designed
to describe the evolution of entropy during the COVID-19 pandemic and the
instantaneous reproductive ratio. We then introduce and use entropy-based
metrics of global transmission to measure the impact and temporal evolution of
a pandemic event. In the formulation of the model, the temporal evolution of
the outbreak is modeled by the master equation of a nonlinear Markov process
for a statistically averaged individual, leading to a clear physical
interpretation. We also provide a full Bayesian inversion scheme for
calibration. The time evolution of the entropy rate, the absolute change in the
system entropy, and the instantaneous reproductive ratio are natural and
transparent outputs of this framework. The framework has the appealing property
of being applicable to any compartmental epidemic model. As an illustration, we
apply the proposed approach to a simple modification of the
Susceptible-Exposed-Infected-Removed (SEIR) model. Applying the model to the
Hubei region, South Korean, Italian, Spanish, German, and French COVID-19
data-sets, we discover a significant difference in the absolute change of
entropy but highly regular trends for both the entropy evolution and the
instantaneous reproductive ratio.
