  The Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model is
one of the standard models of disease spreading. Here we analyse an extended
SEIR model that accounts for asymptomatic carriers, believed to play an
important role in COVID-19 transmission. For this model we derive a number of
analytic results for important quantities such as the peak number of
infections, the time taken to reach the peak and the size of the final affected
population. We also propose an accurate way of specifying initial conditions
for the numerics (from insufficient data) using the fact that the early time
exponential growth is well-described by the dominant eigenvector of the
linearized equations. Secondly we explore the effect of different intervention
strategies such as social distancing (SD) and testing-quarantining (TQ). The
two intervention strategies (SD and TQ) try to reduce the disease reproductive
number, $R_0$, to a target value $R^{\rm target}_0 < 1$, but in distinct ways,
which we implement in our model equations. We find that for the same $R^{\rm
target}_0 < 1$, TQ is more efficient in controlling the pandemic than SD.
However, for TQ to be effective, it has to be based on contact tracing and our
study quantifies the required ratio of tests-per-day to the number of new
cases-per-day. Our analysis shows that the largest eigenvalue of the linearised
dynamics provides a simple understanding of the disease progression, both pre-
and post- intervention, and explains observed data for many countries. We apply
our results to the COVID data for India to obtain heuristic projections for the
course of the pandemic, and note that the predictions strongly depend on the
assumed fraction of asymptomatic carriers.
