  The benefits, both in terms of productivity and public health, are
investigated for different levels of engagement with the test, trace and
isolate procedures in the context of a pandemic in which there is little or no
herd immunity. Simple mathematical modelling is used in the context of a
single, relatively closed workplace such as a factory or back-office where, in
normal operation, each worker has lengthy interactions with a fixed set of
colleagues. A discrete-time SEIR model on a fixed interaction graph is
simulated with parameters that are motivated by the recent COVID-19 pandemic in
the UK during a post-peak phase, including a small risk of viral infection from
outside the working environment. Two kinds of worker are assumed, transparents
who regularly test, share their results with colleagues and isolate as soon as
a contact tests positive for the disease, and opaques who do none of these.
Moreover, the simulations are constructed as a ``playable model" in which the
transparency level, disease parameters and mean interaction degree can be
varied by the user. The model is analysed in the continuum limit. All
simulations point to the double benefit of transparency in maximising
productivity and minimising overall infection rates. Based on these findings,
public policy implications are discussed on how to incentivise this mutually
beneficial behaviour in different kinds of workplace, and simple
recommendations are made.
