The current season that stretches between the Jewish holidays of Pesach/Passover and Shavuot/Pentecost, bounded by סְפִירַת הָעוֹמֶר, is one steeped in numbers. I’ve always had an affinity for this week’s Torah reading which happens to be my Bar Mitzvah portion. It is the opening of what is called “The Book of Numbers” in English, because of the census taken of the Jewish people in the Sinai desert: בְּמִדְבַּ֥ר סִינַ֖י (technically the parsha should be called “Bemidbar” rather than “Bamidbar”). The haftorah begins with numerosity as well, indicating that at some point the census of the Jewish people will approach infinity: וְֽ֠הָיָה מִסְפַּ֚ר בְּנֵֽי־יִשְׂרָאֵל֙ כְּח֣וֹל הַיָּ֔ם אֲשֶׁ֥ר לֹֽא־יִמַּ֖ד וְלֹ֣א יִסָּפֵ֑ר. And it will be that the census of the sons of Israel will be like the sands of the sea, immeasurable and uncountable.
In contrast to the prophetהוֹשֵׁע who predicted unlimited growth constrained by moral principles stands the Malthusian Principle of population curtailment. The rate limiting step for population growth proposed by Malthus was the production of food, but one can substitute Natural Resources to derive a more generalizable model. Malthus believed that nature would correct the imbalance between resources and population growth in the form of disasters such as floods and earthquakes.
Unconstrained infectious disease is a force that curbs population growth, and COVID-19 qualifies as a Malthusian Catastrophe that has presented humanity’s latest inflection point on his graph (inflection through infection, one might say). As the mathematical biologist Kit Yates observed, “much of the story of our history has the often unwritten subplot of contagious disease running through it”. The numbers involved in modeling epidemics and pandemics, the essence of mathematical epidemiology, are a matter of life and death.
As Yates notes in his book published last year in the U.K., any mathematical model is only as good as the assumptions and data underpinning it. For the past century, the S-I-R model has held sway in mathematical epidemiology. This identifies three classes in the population: Susceptibles (people who have not yet had the disease); Infected (those who contracted the disease and could pass it to susceptible); and Removed (people who had the disease and recovered with immunity or those who died from it). In a section entitled “The Next Pandemic”, Yates indicates that for zoonotic viral diseases that jump from nonhumans to humans, and is then transmitted among humans, the model has been expanded to S-C-I-R, with the added class of Carrier. This designation was the class of people capable of passing on the disease while remaining asymptomatic and therefore undetectable in the absence of mass testing of the entire population. Enter COVID-19.
The numbers lead us to the concept of R-0 or R-naught, which is the basic Reproduction profile of the disease in terms of strength or virulence. If a virus has R-0 < 1.0, then the infection will die out quickly as each infectious person passes on the disease, on average, to less than one other individual and the outbreak cannot sustain its own spread. If R-0 is > 1.0, the outbreak is poised to grow exponentially. This is what happened when SARS reached an R-0 somewhere in the range of 2. As reported in early April in the journal Biosafety and Health, the estimated R-0 of SARS 2 or COVID-19 as emanating from Wuhan, China was between 2.43 and 3.10. This led to the ubiquitous mantra you’ve heard about efforts to “flatten the curve” by measures such as masks, hand washing, social distancing, and potential meds/vaccines. This we’ve been told was largely done to avoid overwhelming the healthcare system capacity.
As Yates writes, “once outbreaks are in full swing it is often impractical to develop and test an effective vaccine in time”. Or as Sigal Samuel wrote in Vox last September, we’ve got a bad habit of paying attention to pandemics only when it’s too late. There will be collateral damage unless one is able to adopt an alternative strategy as employed for animal diseases such as culling or “intentional de-population”. Culling is like setting brush fires ahead of rampaging forest fires, a calculated sacrifice of potential susceptible individuals in the SIRS model above. Preventive slaughtering, if you will.
Yates continues: “For active outbreaks of human diseases in unvaccinated populations, culling is clearly not an option. Quarantine and isolation, however, can be extremely efficient ways to reduce the transmission rate and, consequently, the effective reproduction number.” The challenge, as Yates notes, is weighing the economic costs of quarantining healthy individuals against the risk of an enlarged disease outbreak. “It’s impractical in the real world to quarantine a high proportion of the population for a long time”.
Yet here we are, in the real world, having done just that.