  A compartmental epidemic model is proposed to predict the Covid-19 virus
spread. It considers: both detected and undetected infected populations,
medical quarantine and social sequestration, release from sequestration, plus
possible reinfection. The coefficients in the model are evaluated by fitting to
empirical data for eight US states: Arizona, California, Florida, Illinois,
Louisiana, New Jersey, New York State, and Texas. Together these states make up
43% of the US population; some of these states appear to have handled their
initial outbreaks well, while others appear to be emerging hotspots. The
evolution of Covid-19 is fairly similar among the states: variations in contact
and recovery rates remain below 5%; however, not surprisingly, variations are
larger in death rate, reinfection rate, stay-at-home effect, and release rate
from sequestration. The results reveal that outbreaks may have been well
underway in several states before first detected and that California might have
seen more than one influx of the pandemic. Our projections based on the current
situation indicate that Covid-19 will become endemic, spreading for more than
two years. Should states fully relax stay-at-home orders, most states may
experience a secondary peak in 2021. If lockdowns had been kept in place, the
number of Covid-19 deaths so far could have been significantly lower in most
states that opened up. Additionally, our model predicts that decreasing contact
rate by 10%, or increasing testing by approximately 15%, or doubling lockdown
compliance (from the current $\sim$ 15% to $\sim$ 30%) will eradicate
infections in the state of Texas within a year. Extending our fits for all of
the US states, we predict about 11 million total infections (including
undetected), 8 million cumulative confirmed cases, and 630,000 cumulative
deaths by November 1, 2020.
