How has Cummings harmed the fight against coronavirus? Here's the scientific answer

Much of the attention over Dominic Cummings’ family trip from London to Durham has focused on the moral and legal questions. Did his actions obey the letter of lockdown restrictions, which require every person to stay close to home except under severe personal circumstance? And with these restrictions placing an enormous toll on families around the country, was it morally right?

Related: Cummings’ contempt for lockdown rules makes the public feel like fools | Fintan O’Toole

With questions still remaining over some of his assertions, these remain important issues; but even more important is the potential impact of his actions on the behaviour of others. There is evidence that, even with the lockdown rules mostly in place, people are now moving about more frequently, even in the most heavily hit areas of the country.

Partly this change is a consequence of people having a better understanding of the restrictions, and therefore pushing the boundaries. Partly it is likely due to a desire to go out in the warm weather. In Germany, which is well ahead of the UK in controlling coronavirus and easing lockdown, local clusters of infection have arisen due to the resumption of some pre-pandemic activities. This is an almost inevitable outcome of easing restrictions.

While that easing is both justified and necessary, it must be done slowly and with caution. If normal behaviours resume too rapidly, there is potential for the number of Covid-19 cases to increase while our control over its spread remains fragile. In this context, Cummings’ actions have the potential to impede Britain’s recovery from the pandemic.

Intuitively we know that influential people in the public eye can have a profound impact on the behaviour of others. Understanding all this is the domain of game theory, which shows us that when each person simply chooses what seems best for them, the outcome can be terrible for the group. Ironically, Cummings himself has written extensively on this theory. Game theory has been central to the work of many Nobel prize-winners in economics, and it is now widely recognised as important in subjects ranging from evolution to public health, most notably in studying the voluntary uptake of vaccines. This is particularly relevant given the number of “anti-vaxxers” resisting the possibility of being vaccinated against Covid-19.

The success of vaccination relies on enough people taking part to induce herd immunity; and while there may be a small risk associated with taking the vaccine, that risk is outstripped by the benefits of eradicating the disease. However, if too few people take up the vaccine, the benefit of herd immunity is lost, leading to greater infection. What game theory tells us is that mass behaviour has a tipping point: below it, that behaviour is isolated and can ultimately die out; but above it, the behaviour can spread rapidly through the entire population.

Critical to all this is the concept of trust. If a positive behaviour change is required – such as abiding by the lockdown rules – individuals must trust that enough others will do so to make their own sacrifices worthwhile.

The exhortations to stick together – to “stay at home, protect the NHS, save lives” – are a real-world expression of this concept. Each individual action is likely to be small; but each is important because it also influences other people’s behaviour. If we see others obeying a given set of rules, we tend to do the same. This can be very difficult when we do not know people who have had Covid-19, or have not seen how serious it can be. But if even a small number of individuals act with a very different set of values and priorities, it can result in a cascade of selfish behaviour.

The combination of social contact patterns and selfish behaviour can have a profound influence on the ability of a disease to spread, even when those individuals starting the cascade have no more inherent influence than anyone else. There is some evidence from the US that this social connectivity has been important in determining how people adhere to lockdown restrictions. The impact of public figures acting in their personal interest can therefore be disastrous – not because of the individual disease risks they pose, but because of their potential, as a public example, to set off catastrophic behaviour change.

We all hope that Britain has turned the tide against the coronavirus pandemic. However, with no immediate prospects for a vaccine, health services stretched and continued uncertainty over testing and tracing, that success remains fragile. While Cummings’ actions have the potential to undermine that success, what game theory tells us is that we are all influencers. In this sense, it is not only the needs of the many that matter more than the needs of the few, but their actions as well. We cannot change the past actions of others, but our own actions now and in the future are critical for the successful control of Covid-19.

• Rowland Kao is professor of veterinary epidemiology and data science at the University of Edinburgh