An optimal control theory approach to non-pharmaceutical interventions

Lin, Feng; Muthuraman, Kumar; Lawley, Mark

To test the sensitivity of our control policy to the terminal time assumption, we simulated the disease propagation and studied the outcome of applying our NPI policy to settings with an exponential and a gamma terminal time. For each flu scenario specified in the sensitivity analysis, a corresponding NPI policy can be obtained. We randomly selected a value from Exponential(0.0056) and a value Gamma(3, 59.5) as the vaccine arrival time (or simulation terminal time). The sampling was repeated 20 times for each scenario. Then, we simulated the SIRD system starting from an initial state applying the corresponding NPI policy. The simulation was terminated at the sampled vaccine arrival times and the cumulative deaths were recorded. A total of 210 initial states were selected, where s 0 ≥ 80% and i 0 ≤ 20%, for a total of 210, 000 simulations. We studied the difference in cumulative deaths under these two vaccine arrival assumptions. Table 6 lists the descriptive statistics of percentage difference in cumulative deaths for the same initial states at two terminal times. Overall, the difference in cumulative deaths under exponential and gamma terminal times is small (mean = 3.49%). The distribution of difference in cumulative deaths is left-skewed, with 91.8% of these differences being less than 10%. There are a few cases where the cumulative deaths differ significantly (≥ 30%). These cases all started from initial states where only a small Table 5 lists the partial rank correlation coefficients (PRCCs) for the performance measure ω and d T . Table 6 lists the summary statistics of difference in cumulative deaths at exponential and gamma terminal time.