The COVID-19 response team at Imperial college have published a paper on the impact of non-pharmaceutical interventions (NPIs) on the spread of the Corona virus. You can download the paper here:
Non-pharmaceutical interventions are things like forcing people to stay home, closing schools and universities and shutting cafés and restaurants.
The paper makes for some sobering reading. This article gives a brief resumé and a few take-aways.
Caveat: I am not an epidemiologist. The paper is targeted at a non-expert - if mathematically literate - audience. This is a non-expert, but (hopefully) mathematically literate interpretation. If you disagree with my summary or my conclusions then please write in the comments, either here or on the LinkedIn post
The paper is based on a sophisticated epidemiological model that not only takes into account reproduction rates, incubation, symptomatic and asymptomatic infection, recovery, immunity and fatality, but also includes connectivity parameters through a high-resolution population density model that includes regional demographics, class sizes, teacher to student ratios, workplace sizes and commuting distances.
Transmission, mitigation and suppression
The paper distinguishes between mitigation and suppression strategies.
Both strategies seek to reduce the reproduction rate - the number of people an infected person will go on to infect. If this number is less than 1 then the number of new cases will decline over time to low levels, potentially resulting in a complete removal of human to human transmission.
If it is greater than 1 then the number of cases will grow. This growth is initially exponential, which is to say that the number of cases will multiply by a certain factor every day. However, in time, as more and more people are infected and, hopefully, recover, but otherwise die, the reproduction rate will get smaller because there are fewer uninfected people remaining to infect. Eventually there are so few remaining uninfected that the reproduction rate falls under 1 and the number of new cases starts declining. The end state here is the "herd" immunity we've heard so much about in recent days.
Suppression strategies attempt to reduce the reproduction rate to less than 1 and thus reduce new cases to low levels or remove the contagion altogether.
Mitigation strategies attempt to reduce the reproduction rate, but only to slow the growth in the number of cases. Essentially this allows more time for those currently sick and in hospital to get better and make space for the next generation of infected cases.
This is flattening the curve - the goal is only to spread the contagion so that the number of cases requiring hospitalization at any one time is kept below the capacity of the hospitals. This saves lives, because it ensures that people who would die without intense medical attention receive that attention, but it doesn't change the basic dynamics of the epidemic. The contagion still grows until it starts running out of infected cases to infect, after which it falls, and the end number of closed cases is more or less the same.
In the paper, the optimal combination of strategies for mitigation is found to be case isolation, home quarantine and social distancing of over 70s. (These are described in detail in the paper). This is a little confusing as many nations, Denmark included, are taking much more dramatic steps with only mitigation as a goal.
Indeed, the strategies modelled to achieve suppression in the paper - case isolation, household quarantine, generalized social distancing and school and university closure - are currently in place in Denmark in the hope only of achieving some level of mitigation.
With no interventions at all the epidemic peaks in June and has died out by August.
Mitigation - however its achieved - flattens this curve and delays the peak. The more you flatten the curve, the more you delay the peak
The relatively mild mitigation measures modelled peak early July (the flattest of the curves in the figure). These were however deemed woefully inadequate, resulting in demand many times over surge capacity of the health service (red line at the bottom of the graph). Further measures that hopefully further flatten the peak, will inevitably also delay it. If Denmark is seriously only looking to flatten the curve, early July is the earliest it can peak.
When you remove measures, the transmission rebounds. The exact repercussions of this for mitigation aren't clear.
The paper discusses rebound from the removal of measures in the case of suppression. In this, the conclusion is unambiguous. Failure to maintain measures right through to the advent of a vaccine will result in a full rebound in transmission. However, in this case, there is no herd immunity and a large reservoir of uninfected people for the contagion to grow into. What happens when many have already been infected - as would be the case for mitigation, even a successful one - isn't clear.
We might be doing this on and off for a while, but we might not.
One of the scenarios considered in the paper is "adaptive triggering of suppression". Essentially, we suppress now till we get cases well down under capacity. Then we remove measures, but monitor infections. Once infections rise above a certain level, we reintroduce measures. Policies end up being in force around 2/3 of the time.
Again, this is for suppression. How the dynamics of this work for partial herd immunity off the back of a successful mitigated epidemic is not clear. Nor whether it would be necessary.
Professional and informative though the Imperial paper is, it seems either the pandemic has moved on or there's some kind of mismatch between what we're observing, which is driving policy, and the assumptions in the paper.
Certainly in Denmark, and it seems increasingly also in the UK, we are adopting measures that according to the paper should lead to suppression, but which are only adopted in the hope of achieving some level of mitigation. This renders many of the most startling revelations of the paper - the need for triggered suppression, the violent winter rebound, the need to keep measures in place for 18 months - ambiguous because we are no longer looking at suppression as an outcome. We are in for a grim storm in the months to come, but there may be a silver lining in the immunity we win for our pains.
The key unanswered question is then this. When can we start removing measures in the case of a successful mitigation, i.e. a mitigation that keeps us more or less within the capacity of our health service? Can we remove them completely, or will we revert to some milder form. Will we have to monitor and respond along the lines of what is suggested in the paper? What happens when winter comes round again?