Inferring epidemic parameters for COVID 19 from fatality counts in Mumbai
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.