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We introduce a deterministic model that partitions the total population intothe susceptible, infected, quarantined, and those traced after exposure, therecovered and the deceased. We hypothesize 'accessible population fortransmission of the disease' to be a small fraction of the total population,for instance when interventions are in force. This hypothesis, together withthe structure of the set of coupled nonlinear ordinary differential equationsfor the populations, allows us to decouple the equations into just twoequations. This further reduces to a logistic type of equation for the totalinfected population. The equation can be solved analytically and thereforeallows for a clear interpretation of the growth and inhibiting factors in termsof the parameters in the full model. The validity of the 'accessiblepopulation' hypothesis and the efficacy of the reduced logistic model isdemonstrated by the ease of fitting the United Kingdom data for the cumulativeinfected and daily new infected cases. The model can also be used to forecastfurther progression of the disease. In an effort to find optimized parametervalues compatible with the United Kingdom coronavirus data, we first determinethe relative importance of the various transition rates participating in theoriginal model. Using this we show that the original model equations provide avery good fit with the United Kingdom data for the cumulative number ofinfections and the daily new cases. The fact that the model calculated dailynew cases exhibits a turning point, suggests the beginning of a slow-down inthe spread of infections. However, since the rate of slowing down beyond theturning point is small, the cumulative number of infections is likely tosaturate to about $3.52 \times 10^5$ around late July, provided the lock-downconditions continue to prevail.

A reductive analysis of a compartmental model for COVID-19: data assimilation and forecasting for the United Kingdom