  We study the problem of information provision by a strategic central planner
who can publicly signal about an uncertain infectious risk parameter.
Signalling leads to an updated public belief over the parameter, and agents
then make equilibrium choices on whether to work remotely or in-person. The
planner maintains a set of desirable outcomes for each realization of the
uncertain parameter and seeks to maximize the probability that agents choose an
acceptable outcome for the true parameter. We distinguish between stateless and
stateful objectives. In the former, the set of desirable outcomes does not
change as a function of the risk parameter, whereas in the latter it does. For
stateless objectives, we reduce the problem to maximizing the probability of
inducing mean beliefs that lie in intervals computable from the set of
desirable outcomes. We derive the optimal signalling mechanism and show that it
partitions the parameter domain into at most two intervals with the signals
generated according to an interval-specific distribution. For the stateful
case, we consider a practically relevant situation in which the planner can
enforce in-person work capacity limits that progressively get more stringent as
the risk parameter increases. We show that the optimal signalling mechanism for
this case can be obtained by solving a linear program. We numerically verify
the improvement in achieving desirable outcomes using our information design
relative to no information and full information benchmarks.
