SUTRA: An Approach to Modelling Pandemics with Undetected (Asymptomatic) Patients, and Applications to COVID-19

The COVID-19 pandemic that has swept the world has shown a wide variety of behavior across countries, ranging from a gentle rise and gentle fall in India, to multiple waves with each peak higher than its predecessor in the USA, UK, and other countries. It is therefore a challenge to present a unified model that can manifest this wide range of behavior. In this paper, we present a new mathematical model called SUTRA for pandemics that have undetected (asymptomatic) patients, and demonstrate that it does indeed accurately predict the variety of behavior observed during the COVID-19 pandemic. The acronym SUTRA stands for Susceptible, Undetected, Tested (positive), and Removed Approach. There are several novel features of our proposed model. First, whereas previous papers have divided the patient population into Asymptomatic and Infected, we divide patients instead into Tested (T) and Undetected (U). This explicitly accounts for the fact that, due to contact tracing and other such protocols, some fraction of asymptomatic patients do get detected. Second, we introduce a parameter called "reach," to take into account the spatial spread of apandemic over time. Third, we present numerically stable methods for estimating the parameters in our model.We have applied our model to predict the progression of the COVID-19 pandemic in several countries, displaying a variety of behaviors. In all cases, the predictions closely match the actually observed outcomes. In the interests of brevity, we present only the predictions for India.