CoSIR: Optimal control of SIR epidemic dynamics by mapping to Lotka-Volterra System

Abstract

AbstractMultiple macro-phenomena such as disease epidemics, online information propagation, and economic activity can be well-approximated using simple dynamical systems. Shaping these phenomena with adaptive control of key levers has long been the holy grail of policymakers. In this paper, we focus on optimal control of transmission rate in epidemic systems following the widely applicable SIR dynamics. 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 behavior. We exploit this mapping using a control-Lyapunov approach to design a novel adaptive control policy (CoSIR) that nudges the SIR model to the desired equilibrium. Combining CoSIR policy with data-driven estimation of parameters and adjustments for discrete transmission levels yields a control strategy with practical utility. Empirical comparison with periodic lockdowns on simulated and real COVID-19 data demonstrates the efficacy and adaptability of our approach.