  In this article, we consider a dynamic epidemiology model for the spread of
the COVID-19 infection. Starting from the classical SEIR model, the model is
modified so as to better describe characteristic features of the underlying
pathogen and its infectious modes. In line with the large number of secondary
infections not related to contact with documented infectious individuals, the
model includes a cohort of asymptomatic or oligosymptomatic infectious
individuals, not accounted for in the data of new daily counts of infections. A
Bayesian particle filtering algorithm is used to update dynamically the
relevant cohort and simultaneously estimate the transmission rate as the new
data on the number of new infections and disease related death become
available. The underlying assumption of the model is that the infectivity rate
is dynamically changing during the epidemics, either because of a mutation of
the pathogen or in response to mitigation and containment measures. The
sequential Bayesian framework naturally provides a quantification of the
uncertainty in the estimate of the model parameters, including the reproduction
number, and of the size of the different cohorts. Moreover, we introduce a
dimensionless quantity, which is the equilibrium ratio between asymptomatic and
symptomatic cohort sizes, and propose a simple formula to estimate the
quantity. This ratio leads naturally to another dimensionless quantity that
plays the role of the basic reproduction number $R_0$ of the model. When we
apply the model and particle filter algorithm to COVID-19 infection data from
several counties in Northeastern Ohio and Southeastern Michigan we found the
proposed reproduction number $R_0$ to have a consistent dynamic behavior within
both states, thus proving to be a reliable summary of the success of the
mitigation measures.
