Modelling COVID-19 -- I A dynamic SIR(D) with application to Indian data

We propose an epidemiological model using an adaptive dynamic three compartment (with four states) SIR(D) model. Our approach is similar to non-parametric curve fitting in spirit and automatically adapts to key external factors, such as interventions, while retaining the parsimonious nature of the standard SIR(D) model. Initial dynamic temporal estimates of the model parameters are obtained by minimising the aggregate residual sum of squares across the number of infections, recoveries, and fatalities, over a chosen lag period. Then a geometric smoother is applied to obtain the final time series of estimates. These estimates are used to obtain dynamic temporal robust estimates of the key feature of this pandemic, namely the "reproduction number". We illustrate our method on the Indian COVID-19 data for the period March 14 - August 31, 2020. The time series data plots of the 36 states and union territories shows a clear presence of inter-regional variation in the prognosis of the epidemic. This is also bourne out by the estimates of the underlying parameters, including the reproduction numbers for the 36 regions. Due to this, an SIR(D) model, dynamic or otherwise, on the national aggregate data is not suited for robust local predictions. The time series of estimates of the model enables us to carry out daily, weekly and also long term predictions, including construction of predictive bands. We obtain an excellent agreement between the actual data and the model predicted data at the regional level. Our estimates of the current reproduction number turn out to be more than 2 in three regions (Andhra Pradesh, Maharashtra and Uttar Pradesh) and between 1.5 and 2 in 13 regions. Each of these regions have experienced an individual trajectory, which typically involves initial phase of shock(s) followed by a relatively steady lower level of the reproduction number.