COVID-19, R*(1-I) and the difficulty of making policy


Policy is a matter of values and the calculation of cost and benefit.

Take speed limits, for example. Increase the limit, and the severity and number of casualties will rise. Decrease the limit, freedom is curtailed and economic damage done (an economy can’t function at walking pace). Assuming today’s technology, the limit is unlikely to rise beyond 200 mph, or decline below 10 mph. Debate merely nibbles at the edges of the issue – vehicle safety standards, road safety standards and the availability of emergency services, the equitable and orderly provision of which is assumed. It’s hard to imagine any disruption to the ‘not uncomfortable’ equilibrium that current speed limits achieve.

COVID-19 by contrast, is disruptive and governments are struggling to develop policy. But whilst our values are clear (save lives, attend to the sick), the calculation of cost and benefit is both ethically tricky and technically difficult.

The facts are these:

  • COVID-19 is highly contagious. In the absence of social distancing policy the number of individuals (R) to whom, on average, an infected individual is likely to pass on the virus (in the absence of immunity), is almost certainly higher than 2. A value greater than 1 is bad news enough.
  • The proportion of the population immune to COVID-19 (I) is low (current surveillance (antibody) testing suggests it is lower than 0.1 even in countries where thousands have died).
  • COVID-19 is a life-threatening disease (the threat rising with age and ‘underlying health conditions’).
  • There is no cure (though there is hope that drugs might reduce the likelihood of death).
  • There is no vaccine.
  • However, there are treatments that reduce the likelihood of death – oxygen, intensive care, ventilation, etc. These are highly demanding in terms of resources (beds, doctors, nurses, drugs, machinery, PPE, etc.).
  • Those providing treatment (doctors, nurses, etc.) face a disproportionate risk of infection.
  • Reducing social contact lowers R.
  • Unless R*(1-I) is less than 1, cases and deaths will rise exponentially.

This rare and disruptive combination of facts has left governments with no option but to reduce R*(1-I), by means of ‘lockdown’ or ‘social distancing’ policy, to a level that will still enable the provision of treatment to those in acute need in an orderly and equitable manner.

Some individuals have argued that for COVID-19 the ‘cure is worse than the disease’, but for most of us it is unimaginable that treatment could be denied to those who might benefit from it, and that doctors, nurses and care workers should be overwhelmed and placed at high risk of catching the disease themselves.

Imagine if the emergency services could attend just one in every ten car crashes. Most of us (those of us lucky enough to live in a relatively prosperous country) would consider that an unacceptable trade-off of cost and benefit.

The difficult medium-term question (before the arrival of a vaccine and/or high population immunity (I)) is what level of R*(1-I) can be tolerated? How many new cases and deaths are we able to ‘accept’ on a daily basis? As many as our health services can treat? Or far fewer?

  • A value of R*(1-I) higher than 1 means an exponential growth in cases and deaths to a level likely to exceed the capacity of our health services
  • A value of R*(1-I) only just higher than 1 means, perhaps, a manageable growth in cases and deaths, such that, as they expand, health services might still provide treatment in an orderly and equitable manner to those who need it
  • A value of R*(1-I) at 1 means a stable level of new cases and deaths (and as I increases R can also be allowed to rise)
  • A value of R*(1-I) lower than 1 means a decline in cases and deaths, eventually to zero

Assuming that a vaccine for COVID-19 is a year away and that I remains low, most governments will attempt to formulate policies that won’t allow R*(1-I) to grow much higher than 1.

But the first question each government must address is an ethical one. How many cases and deaths averted can be traded for freedoms temporarily curtailed and wealth sacrificed? This isn’t an unreasonable question, even though it’s a difficult one. Just as with speed limits, there must be a ‘not uncomfortable’ equilibrium to find. Don’t forget that we accept a certain level of cases and deaths from seasonal ‘flu without demanding ‘lockdown’ or radical ‘social distancing’.

Indeed, some have argued that COVID-19 is no more serious than ‘flu and that the cure (lockdown of any kind) is worse than the disease. Few, I think, having seen the near-collapse of health systems in prosperous developed countries, even amidst lockdown, would make the same argument today, even if opinions may still differ as to exactly how the trade-off between disease and cure should eventually be made.

Assuming that exponential growth must be prevented at almost any cost, the next questions are technical ones. How, technically, can the ‘acceptable’ level of cases and deaths be reached, and how can R*(1-I) be kept close to 1?

On the whole, governments have taken the first step already. They’ve introduced strict lockdown policies to force cases down to an ‘acceptable’ level (though it’s also imaginable, in cases where governments have acted early, that they might allow cases and deaths to rise to their ‘acceptable’ level). But none, I think, can force cases and deaths down to zero, even if that were their aim.

Once they’ve achieved an ‘acceptable’ level, governments must then devise policies to ‘manage’ R*(1-I) at around 1 for a year or so without recourse to a vaccine. No government knows how to do that yet. Epidemiological theory might help, but only the experimental relaxation of lockdown policies will determine what really works and how, therefore, we are to lead our lives over the coming months. The Czech Republic, Austria, Norway – these countries are selectively relaxing policies. Another two weeks, perhaps, and they will be able to measure the effect on R. Surveillance (antibody) testing will give them the value of I.

The precise level of lockdown that will keep R*(1-I) at 1 may differ from place to place. Some of us may be free to roam, whilst others are confined to their homes. And whilst this is happening there will be those who will argue that R*(1-I) should be allowed to rise beyond 1, if not by very much, to protect the economy. Every government will be forced to answer these difficult questions, and every government will curtail freedoms and sacrifice wealth to some extent. The alternative, of disorder, disruption and the inequitable provision of treatment will always be unacceptable.

The sad thing about all of this is that faster action might have saved many thousands of lives. The stringent lockdown policies aimed at bringing the level of cases and deaths down to an ‘acceptable’ level were unavoidable from day one, but if they’d been implemented sooner (in the UK, or in the USA, for example) that ‘acceptable’ level might have been achieved sooner, and the second phase, of managing R*(1-I), might have already begun, as it has in countries with wiser (and occasionally more authoritarian) governments.

I suspect that countries that come out of this well will be those in possession of some or all of these characteristics:

  • Benign, decisive and mildly authoritarian, government
  • A relatively efficient bureaucracy
  • A well-developed, well-equipped public health service
  • A well-developed infrastructure for disease control
  • Respect for the value of the individual
  • A well-educated population, generally trusting of its government and willing temporarily to sacrifice freedoms and wealth
  • A population culturally capable of social distancing


One more note…

COVID-19 is frequently compared to Spanish Flu, when lockdown at the levels we’re currently experiencing wasn’t even attempted. But there’s one crucial difference, I suspect, between the early 20th century and now, and that is that whilst there were few treatments available for Spanish Flu, there are treatments for COVID-19. I don’t mean cures. I mean that intensive care units, ventilators, even if available only in limited numbers, can be used to save lives. Policy, therefore, can be implemented to ensure that these limited resources are available to those who need them. There were, of course, terrible choices to be made during the Spanish Flu pandemic, but they were subtly different ones. Viruses and the mechanics of contagion were less well understood. Treatments were fewer. Expectations of government and health services were lower. Government was less capable. If you caught Spanish Flu, your chances of survival mightn’t have depended so crucially on the treatment you could receive.