  Epidemic parameters are estimated through Bayesian inference using the daily
fatality counts in Mumbai during the period from March 31 to April 14. A
doubling time of 5.5 days (median with 95% CrI of 4.6-6.9 days) is observed. In
the SEIR model this gives the basic reproduction rate R_0 of 3.4 (median with
95% CrI of 2.4-4.8). Using as input the infection fatality rate and the
interval between infection and death, the number of infections in Mumbai is
inferred. It is found that the ratio of the number of test positives to the
total infections is 0.13\% (median), implying that tests are currently finding
1 out of 750 cases of infection. After correcting for different testing rates,
this result is compatible with a measurement of the ratio made recently via
serological testing in the USA. From the estimates of the number of infections
we infer that the first COVID-19 cases were seeded in Mumbai between late
December 2019 and early February 2020. provided the doubling times remained
unchanged since then. We remark on some public health implications if the rate
of growth cannot be controlled in about a week.
