Control of SIR Epidemics: Sacrificing Optimality for Feasibility

TL;DR

The paper addresses how parameter estimation and state measurement errors affect optimal epidemic mitigation using an isolation-based control within a continuous-time SIR framework. It develops a linear-regression-based parameter estimation method, derives explicit error bounds that depend on the sampling interval $h$ and measurement noise, and proposes a robust control strategy that overestimates epidemic severity to guarantee feasibility under uncertainty. The robust policy delays optimality in exchange for feasibility, and the authors quantify the resulting optimality gap through a bound on the additional isolation cost, which tightens as estimation and measurement accuracy improve. Simulations validate the estimation bounds and demonstrate that the robust strategy can flatten the curve more reliably than the nominal optimum when data are imperfect, with higher isolation costs as a trade-off. Overall, the work provides a principled approach to designing feasible, data-informed epidemic controls when model parameters and measurements are uncertain, offering clear guidance on the trade-offs between feasibility, cost, and performance.

Abstract

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.

Figures (6)

• Figure 1: Comparison of Theorem \ref{['lem:inaccu']} with the Optimal Control Strategy. The figure illustrates the difference between the optimal control strategy and the corresponding spreading process and cost, marked with red lines, and the robust control strategy and its corresponding spreading process and cost, marked with blue lines. The optimal control strategy begins to raise the isolation rate when the infected proportion reaches the infection threshold at time step $t^*_b$. To maintain the number of infected cases at the infection threshold $0.1$, during the outbreak, the optimal control strategy adjusts the isolation rate between $t^*_b$ and $t^*_h$. The isolation rate is then adjusted back to the lowest level after $t^*_h$. In contrast, the robust control strategy adjusts the isolation rate ahead of $t^*_b$, captured by $\hat{t}_b$. This strategy also maintains a higher isolation rate no later than $t^*_h$. Furthermore, the total daily isolation rate of the optimal control strategy is upper-bounded by the daily isolation rate of the robust control strategy. Therefore, the total cost of the optimal control strategy is upper-bounded by the total cost of the robust control strategy.
• Figure 2: SIR Spreading Dynamics
• Figure 3: Parameter Estimation
• Figure 4: Estimation Error and Error Bound without Noise
• Figure 5: Estimation Error and Error Bound with Noisy Data

Theorems & Definitions (16)

• Lemma 1
• Remark 1
• Remark 2
• Corollary 1
• Lemma 2
• Corollary 2
• Corollary 3: Optimal Control Strategy 1
• Proposition 1: Optimal Control Strategy 2
• Definition 1: Robust Control Strategy
• Remark 3