UK Ministers are claiming that any ‘exit strategy’ from lock down will follow the science. However what science can they draw on to determine whether any relaxation of current restrictions will not lead to a resurgence of infections? Scott Moss sets out an approach.

The basic reproduction number R0 has become a well-known concept during the COVID-19 crisis. It is the average number of persons each infected person will infect. Whilst that number is greater than 1, the number of infected persons will continue to grow. If it is less than 1, the total number of actively infected persons will decline, and the epidemic will be under control. R0 is clearly the key indicator of the success of any policy to defeat the pandemic.

The science, in the form of epidemiological models with new data from Italy, allowed the Government to realise that their initial approach to allowing ‘herd immunity’ to develop was a mistake. It would reduce R0 as more people became infected and thus immune, but the projections of death in the meantime were over 250,000.

“it doesn’t take a model to realise that restricting the number of social encounters will reduce the probability of infecting an uninfected person”

Not an acceptable result so ‘following the science’, the Government instituted lockdown.

At no point in this process were any elements of social behaviour included in the models except for assumptions about the probability of an infected person meeting an uninfected person and then the probability of passing on the virus. In actual fact, it doesn’t take a model to realise that restricting the number of social encounters will reduce the probability of infecting an uninfected person and the lower the number of encounters in any time period, the more slowly will the virus spread.

We and the Government turned out to be lucky. Levels of compliance with restrictions were higher than assumed in the model. So far so good.

Now comes the question of relaxing restrictions, the ‘exit strategy’.  What science are they going to rely on now?

For a start, they don’t know the proportion of the population which has been infected as they haven’t done the testing to establish that. There is also uncertainty about how long any immunity lasts after recovery. No information could be more important in planning the relaxations of social restrictions since the greater the proportion of the population that has been infected and the longer the period of immunity, the lower must be R0 and so the faster can be the relaxations.

The Government will also be relying on models using assumptions (otherwise known as guesses) on social behaviour and compliance with relaxed restrictions over what Chief Medical Officer has suggested is going to be quite a long period.

So could they be doing better modelling?

“I was asked to develop social models to analyse how behaviour could be changed to allow for cooperation in restrictions and then their relaxation”

More than 20 years ago, I was asked to develop social models to analyse how behaviour could be changed to allow for cooperation in restrictions and then their relaxation. The context was controlling water use in a drought and the work was commissioned after a major failure in persuading people to control their water use.

In the late 1980s, the water industry in the UK was privatised. The first post-privatisation drought was in 1993. In previous droughts, the public water authorities would issue a set of restrictions on water use. For example, garden watering was restricted or forbidden. Generally these were followed and there were many cases of neighbours reporting one another for violating the restrictions.

After privatisation, the managers of the publicly owned water boards became the managers of the private water companies and their salaries were, at least in the public perception, increased several fold.

As the 1993 drought set in, the usual water restrictions were decreed. At the same time, it became known that more than 40% of mains water was lost through leakage. When this was pointed out to the water companies, the response was that it would be “uneconomic” to repair the leaks. A video of a three-foot-high waterspout that had been gushing for more than a year made the national television news.

“The policy of not repairing leaks was quickly abandoned but the restrictions were still not observed”

The increase in managers’ salaries together with the refusal to spend the money to fix the leaks, had a predictable effect: hardly anyone observed the restrictions and there were no reports to the police of violations. Why should people let their gardens wither and die so that water company managers could have their fat salaries and shareholders their fat dividends? The policy of not repairing leaks was quickly abandoned but the restrictions were still not observed.

After the drought abated and the kerfuffle over leaks and salaries died down, I was asked to produce a model-based account of how the public could be engaged once again to observe restrictions on water use during a drought and also to adopted more water-saving technologies (e.g. less water-using washing machines) and behaviours (e.g., showers instead of baths). The modelling system we used was based on rules of behaviour specified in terms that were close to natural language. The models represented people by collections of rules. The rules determined how the individual would behave in each of a range of situations.

But a given set of rules cannot in general capture behavioural change because if the rules don’t change then the behaviour doesn’t change. So we also had meta-rules. A meta-rule could delete or modify an existing rule and could also write new rules based on an available set of conditions in which a rule might be activated and a set of actions that might be taken. These meta-rules evaluated the existing rules and, from time to time, changed them and, therefore, individuals’ behaviour.

A key element to all of this was that the rules were written in a form that could be understood by stakeholders and, perhaps more important, they were evaluated for plausibility by stakeholders. Our conclusion was that, if the stakeholders’ understanding of the behaviour of individuals was broadly accurate, behaviour could be changed for a few individuals by persuasion and education and if a critical percentage of the population were convinced to accept restrictions, social forces would percolate acceptance through large percentages of the population.

The model was validated in three ways. First, the rules and meta-rules were determined in cooperation with stakeholders and so were deemed plausible. Second, the models produced verbal outputs that were readily converted to natural-language narratives that could be evaluated by stakeholders. Third, the models produced time-series statistics of water demand during simulated droughts. The pattern of changes in water demand seemed unusual in that they exhibited volatile episodes the timing, magnitude and duration of which could not be forecast using any statistical methods. These statistical characteristics were subsequently validated by detailed water consumption data obtained from water metering.

This experience in relation to stakeholder validation and the finding of unpredictable changes in statistical outputs was replicated in other models relating to inflation rates, HIV/AIDS spread, market shares in markets for fast moving consumer goods.

Can such models be used to inform decision-making for the relaxation of social restrictions as the current epidemic is brought increasingly under control? The considerations to be taken into account are far more complicated. In the water-demand case, the only issue was attitudes to water use. In the case of the current crisis, issues turn on anxiety to return to work for social and financial reasons, desire to re-establish direct social contacts, perhaps mental-health considerations, and the unknown likelihood of re-infection and one or more further waves on mass infection.

Unless politicians and scientists involved in making decisions have clear expectations about the effects of relaxation and understand as clearly and as early as possible why those expectations are not being realised, then the process of relaxation will be no better than a crap-shoot.

Scott Moss

Scott, now retired, was research professor and founding director of the Centre for Policy Modelling in Manchester, the inaugural president of the European Social Simulation Association and has led numerous …

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