CoSIR: Managing an Epidemic via Optimal Adaptive Control of Transmission Rate Policy
Harsh Maheshwari and Shreyas Shetty (Flipkart Internet Private Ltd.); Nayana Bannur (Wadhwani AI); Srujana Merugu (Independent)
Abstract: Shaping an epidemic with an adaptive contact restriction policy that balances the disease and socioeconomic impact has been the holy grail during the COVID-19 pandemic. Most of the existing work on epidemiological models focuses on scenario-based forecasting via simulation but techniques for explicit control of epidemics via an analytical framework are largely missing. In this paper, we consider the problem of determining the optimal control policy for transmission rate assuming SIR dynamics, which is the most widely used epidemiological paradigm. We first demonstrate that the SIR model with infectious patients and susceptible contacts (i.e., product of transmission rate and susceptible population) interpreted as predators and prey respectively reduces to a Lotka-Volterra (LV) predator-prey model. The modified SIR system (LVSIR) has a stable equilibrium point, an 'energy' conservation property, and exhibits bounded cyclic behaviour similar to an LV system. This mapping permits a theoretical analysis of the control problem supporting some of the recent simulation-based studies that point to the benefits of periodic interventions. We use a control-Lyapunov approach to design adaptive control policies (CoSIR) to nudge the SIR model to the desired equilibrium that permits ready extensions to richer compartmental models. We also describe a practical implementation of this transmission control method by approximating the ideal control with a finite, but a time-varying set of restriction levels. We provide experimental results comparing with periodic lockdowns on few different geographical regions (India, Mexico, Netherlands) to demonstrate the efficacy of this approach.