P. falciparum takes about thirty-six days, a human case can remain infectious for about eighty days) and some were variable, dependent on circumstances such as which kind of Anopheles mosquito was serving as vector and whether pigs were present nearby to distract thirsty mosquitoes away from humans. MacDonald created equations reflecting his reasonable suppositions about how all those factors might interact. Testing his equations against what was known about the Ceylon epidemic, he found that they fit nicely.
That tended to confirm the accuracy of his suppositions. He concluded that a fivefold increase in the density of Anopheles mosquitoes in relatively disease-free areas of Ceylon, combined with conditions allowing each mosquito relative longevity (sufficient time to bite, become infected, and bite again), had been enough to launch the epidemic. One variable among many, increased by five—and the conflagration was lit.
The ultimate product of MacDonald’s equations was a single number, which he called the basic reproduction rate. That rate represented, in his words, “the number of infections distributed in a community as the direct result of the presence in it of a single primary non-immune case.” More precisely, it was the average number of secondary infections produced, at the beginning of an outbreak, when one infected individual enters a population where all individuals are nonimmune and therefore susceptible. MacDonald had identified a crucial index—fateful, determinative. If the basic reproduction rate was less than 1, the disease fizzled away. If it was greater than 1 (greater than 1.0, to be more precise), the outbreak grew. And if it was considerably greater than 1.0, then kaboom: an epidemic. The rate in Ceylon, he deduced from available data, had probably been about 10. That’s very high, as disease parameters go. Plenty high enough to yield a severe epidemic. But it was the lower side of the range for circumstances such as those in Ceylon. On the upper side, MacDonald imagined this: that a single infected person, left untreated and remaining infectious for eighty days, exposed to ten mosquitoes each day, if those mosquitoes enjoyed reasonable longevity and reasonable opportunities to bite, could infect 540 other people. Basic reproduction rate: 540.
WHO’s eradication campaign failed. In fact, by the judgment of one historian: “It all but destroyed malariology. It turned a subtle and vital science dedicated to understanding and managing a complicated natural system—mosquitoes, malarial parasites and people—into a spraygun war.” After years of applying pesticides and treating cases, the healthocrats watched malaria resurge ferociously in those parts of the world, such as India, Sri Lanka (as then known), and Southeast Asia, where so much money and effort had been spent. Apart from the problem (which proved large) of acquired resistance to DDT among Anopheles mosquitoes, the planners and health engineers of WHO probably gave insufficient respect to another consideration—the consideration of small changes and large effects. Humans have an enormous capacity to infect mosquitoes with malaria. Miss one infected person in the surveillance-and-treatment program to eliminate malarial parasites from human hosts, and let that person be bitten by one uninfected mosquito—it all starts again. The infection spreads and, when its basic reproduction rate is greater than 1.0, it spreads quickly.
If you read the recent scientific literature of disease ecology, which is highly mathematical, and which I do not recommend unless you are deeply interested or troubled with insomnia, you find the basic reproduction rate everywhere. It’s the alpha and omega of the field, the point where infectious disease analysis starts and ends. In the equations, this variable appears as R0, pronounced aloud by the cognoscenti as “R-naught.” (It’s a little confusing, I concede, that they use R0 as the symbol for basic reproduction rate and plain R as the symbol for recovered in an SIR model. That’s just a clumsy coincidence, reflecting the fact that both words begin with the letter R.) R0 explains and, to some limited degree, it predicts. It defines the boundary between a small cluster of weird infections in a tropical village somewhere, flaring up, burning out, and a global pandemic. It came from George MacDonald.
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Plasmodium falciparum isn’t the only malarial parasite of global concern. Outside of sub-Saharan Africa, most human cases are caused by Plasmodium vivax, the second-worst of the four kinds adapted particularly to infecting people. (The other two, P. ovale and P. malariae, are far more rare and not nearly so virulent, causing infections that usually pass without medical treatment.) P. vivax is less lethal than P. falciparum but it does create a lot of misery, lost productivity, and