An optimal control theory approach to non-pharmaceutical interventions

Lin, Feng; Muthuraman, Kumar; Lawley, Mark

We present the computed policies under different transmission characteristics, where it is optimal to activate all NPIs when the system state falls in the control region, Ω1. The optimal policy can be calculated for any combination of flu and cost parameters. We compare the impacts of NPIs triggered at different states, which supports the idea of early containment. For comparison, we present the NPI policies assuming quadratic control cost. The quadratic cost assumption introduces additional complexity into parameter estimation, computation and policy interpretation, thus more research needs to be done to better define the NPI levels and interpret the policy. We perform multivariate sensitivity analysis, which identifies important parameters that affect the intensity of control and the outcome of applying the policy. The findings highlight the importance of establishing a sensitive and timely surveillance system. Finally, we study the outcome of applying our NPI policy under exponential and gamma terminal times, and find small difference in the cumulative death.