An optimal control theory approach to non-pharmaceutical interventions

Lin, Feng; Muthuraman, Kumar; Lawley, Mark

We compare our policy against the most relevant optimal isolation policies derived in [37] . Figures 2(c) and 2(d) show these isolation policies under the different infection rates. The control either isolates at a maximum rate when the number of infectious exceeds a threshold or does nothing. For a pandemic with b = 0.6 and R 0 = 2.0, Figure 2 (d) tells us not to act until the percent infectious exceeds 50%; while Figure 2 (b) tells us to implement NPIs at an earlier stage of the outbreak, for example 99% susceptible and 1% infectious. We illustrate cases for which R 0 > 1, i.e., the uncontrolled infection spreads rather than dying out. Figures 3 (a) and 3(b) compare the epidemic curves with and without NPIs, starting from a state 99% susceptible and 1% infected. According to Figures 2(a) and 2(b) , the NPIs should be triggered at this state. In Figure 3(a) , NPI implementation not only reduces the total death by 62%, but also eliminates the peak of the outbreak. Overall, NPI implementation saves 50% of the average person-days lost. In Figure 3(b) , where a more severe pandemic is considered, the reduction in total deaths is 19% and NPI implementation reduces and delays the peak of outbreak, which allows additional time for vaccine development.