A data first approach to modelling Covid-19

The primary data for Covid-19 pandemic is in the form of time series for the number of confirmed, recovered and dead cases. This data is updated every day and is available for most countries from multiple sources such as [Gar20b, iD20]. In this work we present a two step procedure for model fitting to Covid-19 data. In the first step, time dependent transmission coefficients are constructed directly from the data and, in the second step, measures of those (minimum, maximum, mean, median etc.,) are used to set priors for fitting models to data. We call this approach a “data driven approach” or “data first approach”. This scheme is complementary to Bayesian approach and can be used with or without that for parameter estimation. We use the procedure to fit a set of SIR and SIRD models, with time dependent contact rate, to Covid-19 data for a set of most affected countries. We find that SIR and SIRD models with constant transmission coefficients cannot fit Covid-19 data for most countries (mainly because social distancing, lockdown etc., make those time dependent). We find that any time dependent contact rate decaying with time can help to fit SIR and SIRD models for most of the countries. We also present constraints on transmission coefficients and basic reproduction number<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20110171v2_inline1.gif"/></alternatives></inline-formula>, as well as effective reproduction number<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20110171v2_inline2.gif"/></alternatives></inline-formula>. The main contributions of our work are as follows. (1) presenting a two step procedure for model fitting to Covid-19 data (2) constraining transmission coefficients as well as<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20110171v2_inline3.gif"/></alternatives></inline-formula>and<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20110171v2_inline4.gif"/></alternatives></inline-formula>, for a set of countries and (3) releasing a python packagePyCov19[Pra20b] that can used to fit a class of compartmental models, with time varying coefficients, to Covid-19 data.