It’s possible for a context-sensitive containment strategy to not only work in principle, but in practice, say Karl Friston and Anthony Costello
As the government reveals its roadmap for unlocking England’s nationwide lockdown, a meme has emerged in response: “data not dates.” The roadmap entails a measured and cautious approach to the phased lifting of restrictions—that is underwritten by quantitative measures of vaccination, variants, and viral spread. This approach would be fully endorsed by epidemiologists and control theorists alike—namely, make a move, see what happens, and respond in a way that controls viral spread. Perhaps a useful metaphor here is a thermostat: when things get too hot, switch the heating off—and switch it on again when the temperature falls. This is known as bang-bang control in engineering.
The measured response announced by the government—with four phases, interspersed by several weeks—has the latitude to implement this approach: reopen schools, see what happens, legalise outdoor socialising, see what happens, and so on. So, what are the measures in question?
Several measures are implicit in the four tests that have been adopted: namely, vaccination rollout and efficacy, supplemented with measures of viral spread and evolution. Ultimately, these tests rest upon the prevalence of infection, which speaks to the quantitative criteria used to licence escalation—or de-escalation—of unlocking. This has led some to posit thresholds that would trigger, defer, or revert mitigating restrictions. For example, Independent SAGE has suggested an incidence threshold of 100 cases per 100 000 population for the reopening of schools. At the other end of the scale, a threshold of 10 cases per 100 000 population has been proposed as a criterion for relaxing all exceptional measures (excepting social distancing, mask wearing, etc) in so-called “green zones.” One might ask, where do these thresholds come from?
In part, they reflect received wisdom, and in part, they’re inherited from straightforward epidemiology. If the aim is to preclude exponential growth, then the threshold is simple to specify: when R is one, the incidence of new cases is exactly balanced by the rate at which people recover or die; namely, the prevalence divided by the mean period of infectiousness.* With a period of infectiousness of about five days, the critical incidence is 1/5 of the prevalence. For example, a prevalence of 1% gives a daily incidence of 0.2%—or 200 cases per 100 000 population per day. This could furnish a threshold for opening versus closing schools. However, the implicit bang-bang control will, by construction, not reduce prevalence because prevalence will be maintained at the controlled setpoint of 1%. To implement a suppression strategy—that minimises incidence and prevalence—one can halve the threshold, giving 100 cases per 100 000 population per day.
There are two important aspects of this approach to controlled suppression: first, the incidence threshold—that licences progressive unlocking—depends upon prevalence. Under the above analysis, it is 1/10 of the prevalence. With successful implementation, the prevalence and accompanying threshold will fall, ensuring a graceful transition from an epidemic to an endemic phase. Technically, the endpoint is a minimum-prevalence endemic equilibrium. This could be read as the aspiration of zero covid, where the zero pertains to growth (that may or may not entail zero prevalence). The second key issue is that to implement bang-bang control, one needs real time measures of incidence. Retrospective estimates of R—or long term outcomes like hospital admissions—are not apt because they reflect states of affairs several weeks previously. So, where might these measures come from?
Clearly, they should not be based upon the number of confirmed cases (a.k.a. notification rate), but on estimates of the true incidence and prevalence. This follows because confirmed cases underestimate incidence when prevalence is high—because most cases are missed—and overestimate incidence when prevalence is low—because tests have a finite specificity.** Happily, real time estimates are available, down to the area of (lower tier) local authorities. These estimates are, effectively, the best guess of incidence and prevalence that explains all the data at hand.
Estimates of this sort anticipate a containment strategy that is context sensitive, which can use targeted responses and lifting of restrictions (for example, surge testing, school closures, enhanced support for social isolation, etc.), depending upon the local level of prevalence. This brings us to the final issue: national versus local? A control theoretic approach would suggest that the same principles apply at all scales. This might lead to the paradoxical situation where life could return to normal in many “green zone” local authorities, while the UK remained under quarantine because “red zones” remain somewhere. In fact, this situation is not paradoxical but entirely sensible—and is currently enjoyed by countries like Australia and previously by South Korea, China, and Germany.
Various projections have been made about the number of deaths we can expect to see from further covid-19 surges unless a cautious approach to unlocking is followed. These projections depend upon the timeframe in question; the risk of new variants increasing transmissibility or escaping the vaccine; and upon the success of community based services to find, test, trace, and isolate. If we were able to leverage the untapped efficacy of supported isolation, the “cautious” approach could be the “quickest” to having covid under control.
It’s possible for a context-sensitive containment strategy—based upon real time, prevalence dependent incidence thresholds—to not only work in principle, but in practice. We can see this by the example of countries that have successfully suppressed viral spread.
Karl J Friston, scientific director, Wellcome Centre for Human Neuroimaging. Karl is also a professor at the Queen Square Institute of Neurology, University College London, and an honorary consultant at The National Hospital for Neurology and Neurosurgery.
Anthony Costello, professor of global health and sustainable development, UCL Institute for Global Health, University College London.
Competing interests: Karl Friston and Anthony Costello are both members of Independent SAGE. They declare no other conflicts of interest or competing interests.
* Under a simple SIR model this would correspond to the serial interval.
** For example, with a specificity of 99% and zero prevalence, when testing 1% of the population a day, one would expect 10 confirmed cases per hundred thousand per day, 70 per hundred thousand per week, or a 14 day notification rate of 140 per hundred thousand.