Abstract
The benefits of different levels of engagement with test, trace and isolate procedures are investigated for a pandemic in which there is little population immunity, in terms of productivity and public health. 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 also analysed in the continuum limit. All simulations point to the double benefit of transparency in both maximizing productivity and minimizing overall infection rates. Based on these findings, public policy implications are discussed for how to incentivise this mutually beneficial behaviour in different kinds of workplace, and simple recommendations are made.
Highlights
This study is inspired by the situation in the UK in the latter half of 2020 as the nation has been attempting to restart the economy in the aftermath of the first COVID-19 virus infection peak
The fundamental model is a dynamic network with N nodes, in which nodes are workers and the state at node i is a 3-tuple: Xi 1⁄4 (xi, pi, oi); xi [ {S, E, A, U, Q, R}, pi [ {0, 1}, oi [ {0, 1}: xi gives the disease state; pi is a binary variable that measures whether the worker is present in the workplace or is self-isolating at home; oi is a binary variable that determines the opacity of the worker, namely whether they consistently engage in test, trace and isolate and share their data openly, or not
Represent the time of infection and proportion of opaque individuals, respectively, δ is the proportion of people who gain immunity upon recovery and d/N represents the chance that two individuals are connected within the workplace
Summary
This study is inspired by the situation in the UK in the latter half of 2020 as the nation has been attempting to restart the economy in the aftermath of the first COVID-19 virus infection peak. There has been much recent evidence to suggest that the most effective containment measure in a human epidemic with relatively small proportions of infectious individuals is that of rapid testing, contact tracing and isolation of those in the contact group [1,2]. Given a small overall rate of viral infection, an employer might seek to maximize the workplace productivity by staying open, without isolation of exposed workers Such actions would clearly compromise safety, and are negative to society as a whole. If every workplace took this attitude, clearly resurgence within the general population would be probable, whereas one or two isolated ‘bad apple’ employers might be able to benefit by maximizing their personal productivity, provided that others do not This ‘bad apple’ principle has been analysed in the context of epidemics by Enright & Kao [12], who ran an agent-based simulation where there are precisely such conflicting pay-offs.
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