Which lockdowns are the best lockdowns? Optimal interventions and the trolley problem in heterogeneous populations (preprint)

ABSTRACT

Interventions to mitigate the spread of infectious diseases, while succeeding in their goal, have economic and social costs associated with them. These limit the duration and intensity of the interventions. We study a class of interventions which reduce the reproduction number and find the optimal strength of the intervention which minimises the attack rate of an immunity inducing infection. The intervention works by eliminating the overshoot part of an epidemic, and avoids a second-wave of infections. We extend the framework by considering a heterogeneous population and find that the optimal intervention can pose an ethical dilemma for decision and policy makers. This ethical dilemma is shown to be analogous to the trolley problem and we discuss how the dilemma can be avoided.