Some thoughts on the Imperial College modelling paper
I know that the findings of this paper have been discussed at length, but I thought it might be worth saying a bit more about how the model works and identifying the assumptions it makes, some which I found quite surprising.
How the model works: a simulation based on a virtual world
The authors adapted an existing simulation model used to support pandemic influenza planning. They use census and other data to create an artificial world that closely maps to Britain (and the US). They created households with an age and size structure based on census data, with an artificial school network based on numbers of children in those households. Artificial workplaces were created based on workplace distribution data and individuals are assigned to these schools and workplaces based on location and commuting distance data.
Transmission occurrred through contacts made with infectious individual either within the household, at work/school or randomly in the community (transmission in the community depended on population density). It works out that transmission occurs roughly equally across split:
— households
— school/work
— community
and this split accords with social mixing surveys.
Assumptions
· R0 = 2.4 (R0 is the number of new people each infected person goes on to infect). This is based on early Wuhan data.
· Doubling time = 5 days. This is almost certainly an underestimate (I think it comes from the influenza rate in the original model; I have heard three days quoted for SARS-COV-2)
· Symptomatic cases are more infectious than asymptomatic cases; 2/3 are symptomatic enough to be spotted for home quarantine.
· The model was "seeded" with enough infected individuals to give the number of cumulative deaths seen in the GB or US by 14 March 2020
· 4.4% of infections are hospitalised
· 0.9% of infections die
· 30% of hospitalised cases require intensive care
· 50% of intensive care cases die
This is all varied by age of infected person, shown in the table below:
The authors let these assumptions play out in the absence of any control measures (or spontaneous changes in individual behaviours). They predict 81% of the population would be infected over the course of the epidemic
The vast majority of cases occur within 3 months
This would create 510,000 deaths in GB, based on the false assumption that the health system isn't overwhelmed.
Yet at the peak, the model predicts that only 1 in 30 cases that needed one would get an intensive care bed.
Note: something doesn’t seem right about these assumptions. 0.9% mortality assumes there are enough intensive cared beds. Let’s assume there are none. Since 50% of those in intensive care are assumed to die, the maximum death rate (assuming all without such a bed die) is 1.8%. Yet we know around 3% died in Wuhan, and a higher rate still in Italy. Any thoughts on this issue?
Okay, that is the Do Nothing scenario.
Mitigation scenario (“flatten the curve”)
Control measures
The model then looks at the effect of 5 non-pharmaceutical controls measures, and there effect following the “mitigation” strategy originally adopted by the UK gov. They are, with compliance rates:
CI - case isolation in the home for 7 days.
70% comply
HQ - Quarantine of whole household for 14 days where anyone in it has symptoms 50% or household comply.
50% comply
SDO - Social distancing of those aged over 70.
75% comply
SD - Socia distancing of the whole population. 100% comply: 75% reduction in community contacts, 25% increase in home contacts.
PS - Closure of all schools and 75% of universities
Full details
Here is how mitigation plays out in the model. Note the red line of critical care bed capacity at the bottom of the graph.
Figure 2: Mitigation strategy scenarios for GB showing critical care (ICU) bed requirements. The black line shows the unmitigated epidemic. The green line shows a mitigation strategy incorporating closure of schools and universities; orange line shows case isolation; yellow line shows case isolation and household quarantine; and the blue line shows case isolation, home quarantine and social distancing of those aged over 70. The blue shading shows the 3-month period in which these interventions are assumed to remain in place.
Using the strictest combination that the authors modelled (case/household quarantine plus social distancing for the over 70 and chronically sick; no overall SD or school/uni closure) gives 250,000 deaths (see appendix table 1A). This assumes unlimited intensive care beds, even though at peak only 1 in 8 of those that needed one could have one.
I can only assume the authors made no attempt to model the real likely number of deaths to spare the government’s blushes, since they admit their assumption does not hold.
NEXT: suppression strategy.