An optimal control theory approach to non-pharmaceutical interventions

Lin, Feng; Muthuraman, Kumar; Lawley, Mark

Mathematical models are often used to study disease spread, with the Susceptible-Infectious-Recovered (SIR) model being preferred for diseases spread via droplet and aerosol. The SIR model has been used to study pandemic flu [11, 12, [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] , seasonal flu [26] [27] [28] , SARS [13, [29] [30] [31] , and smallpox [32] [33] [34] [35] . These papers use SIR to simulate the disease outbreak and evaluate the effectiveness of selected control measures under various predefined scenarios. They do not provide optimal controls for initiating implementation, and thus we will not review them here. SIR literature most directly relevant to this work includes [36] [37] [38] [39] [40] [41] . These authors use the SIR model to study optimal controls, i.e., controls that minimize a prescribed objective function. Most show "bangbang" controllers to be optimal (in the sense of minimizing a specified objective function). These policies apply no control until the occurrence of a triggering event and then apply controls at maximum strength.