Mathematical models have been used throughout the COVID-19 pandemic to help plan public health measures. Attention is now turning to how interventions can be removed while continuing to restrict transmission. Predicting the effects of different possible COVID-19 exit strategies is an important current challenge requiring mathematical modelling, but many uncertainties remain.

In May 2020, Oxford Mathematician Robin Thompson met with other mathematical modellers and scientists online at the 'Models for an Exit Strategy' workshop, hosted by the Isaac Newton Institute in Cambridge. Two of the other researchers are also based in Oxford (Prof. Christl Donnelly and Prof. Deirdre Hollingsworth). Many of the participants are providing evidence to governments worldwide during the pandemic. The workshop therefore gave an opportunity to summarise and discuss current open questions that, if answered, will allow the effects of different exit strategies to be predicted more accurately using mathematical models.

Three main research areas were outlined as requiring attention:

First, parameters governing virus transmission must be estimated more precisely. For example, statistical methods for estimating the time-dependent reproduction number ($R_t$) must be extended to include additional features. The value of $R_t$ represents the expected number of secondary cases generated by someone infected at time t, and changes continually during any epidemic.

Second, heterogeneities in transmission must be understood more clearly. Models can be constructed that include different types of heterogeneity, including spatial heterogeneity (which can be represented in network or household models) and age-dependent transmission.

Third, there must be a concerted effort to identify data requirements for resolving current knowledge gaps, particularly (but not exclusively) in low-to-middle-income countries. Models can be used not only to make predictions using limited available data, but also to reveal which data must be collected in order for more accurate predictions to be made.

These key challenges for improving predictions of the effects of different COVID-19 exit strategies are outlined in this paper which was published in the journal Proceedings of the Royal Society B in August 2020. The challenges that are outlined require mathematicians to work with a diversity of other scientists and policy-makers as part of a global collaborative effort. This collaboration is of critical importance for shaping public health policy to counter this pandemic and those in the future.


Fig 1 (above): the transmission risk depends on the frequency of contacts between individuals and the transmission probability per infected-susceptible contact. This graph shows the average number of daily contacts between an individual in the age group on the x-axis and a contact in the age group on the y-axis, in the UK under normal circumstances (data from Prem et al. PLoS Comp Biol 13: e1005697, 2017). Figure generated by Francesca Lovell-Read (DPhil student in Oxford Mathematics' Wolfson Centre for Mathematical Biology).

Fig 2 (above): the main goal of any COVID-19 exit strategy is to relax public health measures without risking a surge in cases (like the one shown here).


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