Control of SIR Epidemics: Sacrificing Optimality for Feasibility

We study the impact of parameter estimation and state measurement errors on a control framework for optimally mitigating the spread of epidemics. We capture the epidemic spreading process using a susceptible-infected-removed (SIR) epidemic model and consider isolation as the control strategy. We use a control strategy to remove (isolate) a portion of the infected population. Our goal is to maintain the daily infected population below a certain level, while minimizing the resource captured by the isolation rate. Distinct from existing works on leveraging control strategies in epidemic spreading, we propose a parameter estimation strategy and further characterize the parameter estimation error bound. In order to deal with uncertainties, we propose a robust control strategy by overestimating the seriousness of the epidemic and study the feasibility of the system. Compared to the optimal control strategy, we establish that the proposed strategy under parameter estimation and measurement errors will sacrifice optimality to flatten the curve.