  We introduce a deterministic model that partitions the total population into
the susceptible, infected, quarantined, and those traced after exposure, the
recovered and the deceased. We hypothesize 'accessible population for
transmission of the disease' to be a small fraction of the total population,
for instance when interventions are in force. This hypothesis, together with
the structure of the set of coupled nonlinear ordinary differential equations
for the populations, allows us to decouple the equations into just two
equations. This further reduces to a logistic type of equation for the total
infected population. The equation can be solved analytically and therefore
allows for a clear interpretation of the growth and inhibiting factors in terms
of the parameters in the full model. The validity of the 'accessible
population' hypothesis and the efficacy of the reduced logistic model is
demonstrated by the ease of fitting the United Kingdom data for the cumulative
infected and daily new infected cases. The model can also be used to forecast
further progression of the disease. In an effort to find optimized parameter
values compatible with the United Kingdom coronavirus data, we first determine
the relative importance of the various transition rates participating in the
original model. Using this we show that the original model equations provide a
very good fit with the United Kingdom data for the cumulative number of
infections and the daily new cases. The fact that the model calculated daily
new cases exhibits a turning point, suggests the beginning of a slow-down in
the spread of infections. However, since the rate of slowing down beyond the
turning point is small, the cumulative number of infections is likely to
saturate to about $3.52 \times 10^5$ around late July, provided the lock-down
conditions continue to prevail.
