An optimal control theory approach to non-pharmaceutical interventions

Lin, Feng; Muthuraman, Kumar; Lawley, Mark

influenza characterized by b = 0.4 and R 0 = 1.33. Figure 4 (a) shows a multi-level policy in which NPIs are applied at varying strength levels based on certain state criteria. Note that "red" indicates > 80% NPI strength, "yellow" indicates 60 80% NPI strength, and so forth. The level of NPI policy decreases from 100% of maximum NPI level to 0% as system state traverses from the upper to the lower part and from the right corner to the interior region. The contour line at u* ≈ 50% of maximum impelmentation level is very similar in shape and location to the boundary between Ω1 and Ω2 in Figure 2 (a). As another demonstration, Figures 4(b) and 2(b) show the control policies under both control costs with influenza characterized by b = 0.6. The two boundaries between Ω1 and Ω2 in Figure 2 (b) resemble the contour lines u* ≈ 50% of maximum impelmentation level in Figure 4 (b). The two regions of high level of u* in the upper corner and lower right corner of Figure 4 (b) correspond to two control regions Ω1 in Figure 2 (b). In addition, Table 2 compares the means of the expected person-days lost per person due to death, D , and control intensity, u *, between the linear and quadratic models. The overall NPI strength of the linear model is higher than that of the quadratic model, while the expected person-days lost due to death is lower. The linear model tends to implement NPIs more intensely and save more lives while having a higher overall cost.