An optimal control theory approach to non-pharmaceutical interventions

Lin, Feng; Muthuraman, Kumar; Lawley, Mark

Moreover, the linear cost model appears to place more weight on death, thus implementing more control and saving more lives as shown in Table 2 . In cases with quadratic cost structure, using a linear model might result in over-control which would not be marginally effective. However, quadratic cost introduces additional complexity in parameter estimation, computation, and policy interpretation. For example, we must determine how to implement NPIs at X% of maximum. This requires determining which NPIs will be implemented for each control level. The bang-bang policy, on the other hand, has only two levels, which is easier to understand and implement. Finally, it is not clear that a direct comparison between policies obtained under linear and qudratic cost structures is appropriate, because the value functions are defined differently. More research needs to be done to better define the NPI levels and interpret the policy if a non-linear cost function is chosen.