Over the last months, many publications (in the news, in scientific journals etc.) have claimed that drastic social measures are needed in order to control the spread of the infamous COVID-19. However, a different analysis of the situation may provide us with a more optimistic outlook. Indeed, in a recent paper on superspreaders, we suggest that a simple mathematical perspective on the trends may show that the virus can die out on its own without infecting high percentage of the population. The best way to handle the current crisis is therefore, in our opinion, to focus on the superspreaders and we show mathematically why.
While it is tempting to look for correlations between the biological aspects of the virus and its spread, we attempt to show that this may be unnecessary, for mathematical reasons.
It is estimated by some research that a small fraction (say less than 10%) of the infected population cause almost all the rest of the infection (including those immediately infected as well as their very close contacts, such as family members). These are the above-mentioned superspreaders.
Just as social media influencers are mostly responsible for the spread of trends or as 80% of the world money is in the hands of a 20% happy few, 5 to 10% of the infected individuals would be responsible for 80% of the infections. These individuals play a vital role in the spreading process.
We suggest as a first hypothesis that the reason why these individuals are overly contagious should be attributed to social causes rather than to biological ones: they tend to have a higher number of social contacts (due to their social or professional lifestyle), and are thus more likely to be infected with the virus; in turn, they have higher chances to infect others, both directly and indirectly.
Therefore, one might ask whether one really needs to find a biological explanation to some trends of the spread, or, in other words, whether these facts really do require an explanation at all: if the spread decreases with time due to network/interaction reasons, there is no reason to look for other explanations. It is generally acknowledged that the nature of human interaction is heterogeneous and that the number of contacts behaves according to the Pareto distribution or power law (when the network is scale-free). To put it simply: this happens when few have a high number of contacts while most have a small number of contacts. Those explanations should be considered before seeking differences in the way people sneeze.
Until now, the expected number of secondary infections has been measured through the (in)famous parameter R0, which provides us with the average number of people infected by one infected individual. In other words, it tells us, on average, how many people can one single individual infect. It is generally assumed that the disease will die out on its own in case R0<1, or will cause a large fraction of the population to be infected in case R0>1, until many will become immune (assuming that one infection is enough to immunize the subject, as seems to be the case).
When the disease starts its spread, superspreaders play a vital role, and heavily contribute to the reproduction parameter. One way the disease may die out—much before large fraction is infected—is because those superspreaders are out of commission well before regular spreaders. Being likely to be highly susceptible to the virus, they therefore become immune early. Once their contribution to the reproduction parameter is eliminated, it is quite plausible for R0 to decrease below 1, which will mean that the disease will eventually disappear.
Consequently, if one accepts that individuals have considerably different probability of being infected (and to infect), they should be weighted differently when calculating the global infection distribution. There is indeed a strong correlation between the probability of being infected and the average number of secondary infection—which we claim there is, and which we have demonstrated here and here. If one looks at the distribution through the lens proposed in these papers, one will accept that it is natural for R0 (or possibly another parameter S0 being the effective spread) to change with time, and in particular to dramatically decrease, well before general immunity is reached. To put it differently, the spread could slow down with a much lower fraction of infected individuals than is usually anticipated.
The political efforts to contain the spread have included stringent measures such as general quarantines which have had a negative impact on the economical and social situation. In reality, the reproduction parameter starts high, when superspreaders have their strong affect, and decrease as the spread progress. In reality, the reproduction parameter starts high, when superspreaders have their strong effect, and decrease as the spread progress. This strongly suggests the possibility of the parameter decreasing below 0 much before a large fraction of the population being infected.
Taking measures reducing the superspreaders’ impact would certainly dramatically improve the situation, without causing the substantial disruption to individual rights and economy due to lockdowns globally. For the sake of comparison, if a forest was to be on fire in some un-located points, instead of flooding the whole forest, would it not be more sensible to locate those points first (in this case, the superspreaders) and deal with them locally?
There are various ways to reduce the superspreaders’ effect: for instance, once a small group of potential superspreaders has been identified (these could be hospital, supermarket, school, and public transportation employees), they should undergo frequent COVID tests as well as antibody test. Those proving to be immune should be free to interact with the public. In addition, interaction within small groups such as school population should be limited.
This could have two types of impact: first, it could (hopefully) reduce the effective R0 below 1, in which case the pandemic would stop without hitting a large portion of the population; second, it could decrease the spread rate of the disease. This could in turn allow us more time to weigh out potential reactions and measures.
Before closing our first Corona post, lets us ponder some questions:
– What is the exact goal of the social measures taken, and what is the best strategy to achieve that goal? These two questions are crucial but little discussed, and when debated, the answers widely vary. Let us assume for sake of this discussion the highly likely option that a large-scale immune treatment is years away.
– What should one presume regarding the network of contacts?
– Is R0 the real parameter to take into account in typical networks?
The real challenge is now to examine the valid options at our disposal by looking at the facts without letting our judgement be clouded by unfounded assumptions.