Optimal control strategies in epidemic models: analysis of community and traveler isolation strategies under resource constraints

Abstract

In some regions, health authorities may implement an elimination strategy involving public health measures that apply to travelers and community members to control infectious disease spread. Optimal control theory consists of mathematical results that apply to epidemiological models and describe control strategies that maximize or minimize an epidemiologically-relevant quantity given constraints. The previous work of Hansen and Day (2011) has characterized optimal controls involving community isolation and vaccination with the objective of minimizing outbreak size. We build on this previous work by considering epidemiological dynamics involving infection importation, traveler isolation as a control measure, and by characterizing the optimal controls in the terminology of public health. We discuss a related theorem from Hansen and Day (2011) in the context of our extensions of their modelling. We numerically implement control measures and characterize the resulting epidemiology and resource use as an elimination, mitigation, or circuit breaker strategy. We find that which public health strategy the implemented control is characterized as depends on parameter values that can be interpreted as corresponding to regional conditions. When resources are not limited, the implemented strategy corresponds to: an elimination strategy, when the maximum daily isolation rate is high and the importation rate is low; and a mitigation strategy, when the maximum daily isolation rate is low and the importation rate is high. When resources are limited, the implemented strategy corresponds to a circuit breaker strategy. No previous studies have provided a general framework whereby elimination, mitigation, or circuit breaker strategies can arise as solutions to optimal control problems for different epidemiological and resource use-related parameters, and such results show that different infectious disease control strategies can be optimal in different regions.