An optimal control theory approach to non-pharmaceutical interventions

Lin, Feng; Muthuraman, Kumar; Lawley, Mark

We sampled ranges of the parameters 1000 times using Latin Hypercube Sampling (LHS) to generate 1000 scenarios [46] [47] [48] . Then we conducted multivariate uncertainty and sensitivity analysis to determine the uncertainty in the performance measure that was due to the uncertainty in estimating the input parameters. The descriptive statistics for ω and d T are given in Table 4 , which lists the mean, variance, median, minimum, and maximum of ω and d T . Figure 5 shows the empirical cumulative distribution functions (CDFs) of ω and d T obtained from 1000 LHS scenarios and Table 5 provides the partial rank correlation coefficients (PRCCs) for the performance measures and each parameter. The CDF of ω revealed a wide range of estimates due to the uncertainty in estimating the values of the five input parameters. Sixty percent of ω estimates are less than 2.3%, with a minimum of 0% and a maximum of 98.7%. For ω, the PRCCs are all statistically significant, i.e. p < 0.05. The cost of NPI implementation, c, the time when a death occurs after infection, 1/τ, and the time for an infectious person to recover, 1/g, are the most statistically influential (|PRCC| > 0. 5 ). An increase in c or 1/τ corresponds to a decrease in ω; while an increase in the infection period 1/g corresponds to an increase in ω.