In Part 4, we talked about Extreme Value Theory and its relevance to overdispersion. In this section, we talk about the implications of COVID-19 overdispersion to epidemiology.
A good place to start is Althouse (@BMAlthouse) et al’s (doi.org/10.1371/journa) 10,000 simulations of NB Dist spread (R0=2.6, k=0.16).
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Red dotted line = spread as if 2.6x per generation
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Yellow line = mean for sims taking off
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Blue line = mean for sims contained
These simulations show that overdispersion ==> 2 disparate scenarios: infection actually becomes extinct OR spread is explosive (more than uniform R0 spread). NOTE: these simulations may underestimate explosive spread: NBDist does not model superspreader events well – see Part 4
The reason for this is that overdispersion has 2 diametrical realities:
1. Large majority of COVID cases do NOT lead to secondary transmissions.
2. COVID lead to uncommon, yet significant superspreading events (SSE) that can drive population-level spread
These diametric, opposing realities (#1 vs. #2) lead to a push-pull dynamic – whichever dominates is what determines the overall outcome. When we let Reality #1 > #2, epidemic can be contained. This is why overdispersion can actually be advantageous. As shown by Lloyd-Smith nature.com/articles/natur, greater dispersion (smaller k) has higher probability of extinction across mult R0.
Japan, in particular, has been good about taking full advantage of this strategy. By avoiding 3Cs (Closed, Crowded, and Close-contact settings), it has ensured that #1>#2: most cases have zero trans, and SSEs remain low, despite not really having aggressive lockdown.
However, when #2>#1, we risk the “tail wagging the dog” and explosive spread becomes the norm. In the USA, sadly, we have had one SSE after another. In Boston, for instance, in 1st wave in March, we saw a bump after infamous Biogen Conf (known SSE: nytimes.com/2020/12/11/us/)
And it was actually another SSE: rush of travelers returning from Europe to avoid being locked out by travel ban (3/13) that likely led to even a greater surge in our hospital. @MassDPH data supports the importance of travel (and 2nd local transmission) at the time.
Sturgis Rally is another example of how SSE may have driven epidemiological dynamics.
Push-pull dynamics (#1 vs #2) explains for seemingly random nature of the COVID outbreaks. See @BMAlthouse pub doi.org/10.1371/journa. E.g., why out 16 +cases in Ohio jails, just 3 had large outbreaks; why initial outbreaks occurred in smaller cities, not large ones.
Naturally, COVID-19 overdispersion suggests that we maximize #1 (Zero transm), minimize #2 (SSE) and, thru them, develop a more targeted response. My concern is that we have focused so much on latter (decr #2) that we have neglected maximizing #1.
For example, in Massachusetts, emphasis on minimizing SSEs have encouraged more people to stay at home, but this also means COVID+ cases will more likely infect the household (and thus decrease Zero transmissions #1). In Massachusetts, Household setting make the bulk of transmission.
Similarly, for new “UK variant” SARS-CoV2 B.1.1.7, this variant arose in multiple localities despite being in lockdown. Is it possible that this variant is particularly effective in reducing dispersion in this setting? Reversing the Zero-transmission that COVID is known for?
So the dynamic increase in this variant may be attributed to an imbalance arising during the lockdown: Benefit in reducing SSE (#2) is outweighed by the reduced chance of Zero transm at home (#1) ==> leading to overall R0 >1.
Maybe, we should focus on how B.1.1.7. may be particularly efficient at home transmission? One possibility is that younger population may be playing a bigger role here. See Pre-print by @erikmvolz and @neil_ferguson (https://t.co/fwWz7wjjTC?amp=1)
In summary, overdispersion has 2 diametric realities: #1 Zero-tranms and #2 SSE. The push-pull dynamics explains for divergent successes between countries (e.g., USA vs. Japan) and seemingly random nature of COVID spread. Containment is best when both realities are recognized.
In next section, we will discuss possible causes of the COVID-19 overdispersion.