Spillover: Animal Infections and the Next Human Pandemic (18 page)

Their caveat: If that’s so, the great dream of malaria eradication becomes even less attainable. Krief and company didn’t press the point but you might read that to mean: We can’t hope to kill off the last parasite until we kill off (or cure) the last bonobo.

But wait! Still another study of
P. falciparum
origins, published in late 2010, pointed to still another candidate as its prehuman host: the western gorilla. This work appeared as a cover story in
Nature,
with Weimin Liu as first author and major contributions from the laboratory of Beatrice H. Hahn, then at the University of Alabama at Birmingham. Hahn is well known in AIDS-research circles for her role in tracing the origins of HIV-1 among chimpanzees, and for developing “noninvasive” techniques of sampling for virus in primates without having to capture the animals. Simply put: You don’t need a syringe full of blood if a little poo will do. Fecal samples can sometimes yield the necessary genetic evidence, not just for a virus but also for a protist. Applying those techniques to the search for plasmodium
DNA, Liu, Hahn and their colleagues were able to gather far more data than were previous researchers. Whereas the Krief group had looked at blood samples from forty-nine chimpanzees and forty-two bonobos, most of which were captive or confined within a sanctuary, Liu’s group examined fecal samples from almost three thousand wild apes, including gorillas, bonobos, and chimps.

They found that western gorillas carry a high prevalence of plasmodium (about 37 percent of the population is infected) and that some of those gorilla parasites are nearly identical to
P. falciparum.
“
This indicates,
” they wrote confidently, “that human
P. falciparum
is of gorilla origin, and not of chimpanzee, bonobo or ancient human origin.”

Furthermore, they added, the entire genetic range of
P. falciparum
in humans forms “
a monophyletic lineage within the gorilla
P. falciparum
radiation
.” In plain talk: The human version is one twig within a gorilla branch, suggesting that it came from a single spillover. That’s one mosquito biting one infected gorilla, becoming a carrier, and then biting one human. By delivering the parasite into a new host, that second bite was enough to account for a zoonosis that still kills more than a half million people each year.

26

M
athematics to me is like a language I don’t speak though I admire its literature in translation. It’s Dostoyevsky’s Russian, or the German of Kafka, Musil, and Mann. Having studied calculus hard in school, as I did Latin, I found that the deep knack wasn’t in me, and the secret music of differential equations fell wasted on my deaf ears, just like the secret music of
The Aeneid.
So I’m an ignoramus, an outsider. That’s why you should trust me when I say that two other bits of mathematical disease theory, derived from early twentieth century concerns over epidemic malaria and other outbreaks, are not only important but intriguing, their essence quite capable of comprehension by the likes of you and me. One came out of Edinburgh. The other had its roots in Ceylon.

The first bit was embedded in a 1927 paper titled “A Contribution to the Mathematical Theory of Epidemics,” by W. O. Kermack and A. G. McKendrick. Of these two partners, William Ogilvy Kermack has the more memorable story. He was a Scotsman, like Ross and Brownlee, educated in mathematics and chemistry before he began his career doing statistical analyses of milk yields from dairy cows. Every poet hears his first nightingale somewhere. Kermack went from milk yields into the Royal Air Force, emerged after brief service to do industrial chemistry as a civilian, and then around 1921 joined the Royal College of Physicians Laboratory in Edinburgh, where he worked on chemical projects until a lab experiment blew up in his face. I mean that literally. He was blinded by caustic alkali. Twenty-six years old. But instead of becoming an invalid and a mope, he became a theoretician. Gathering back resolve, he continued his scientific work with the help of students who read aloud to him and colleagues who complemented his extraordinary capacity for doing math in his head. Chemistry led Kermack into the search for new antimalarial drugs. Mathematics engaged him on the subject of epidemics.

In the meantime Anderson G. McKendrick, a medical doctor who had served in the Indian Medical Service (again like Ross), became superintendent of the Laboratory of the Royal College of Physicians and therefore in some sense Kermack’s boss. On a level transcending hierarchy, they meshed. Sightless yet unquenchably curious, Kermack later worked on various subjects, such as comparative death rates in rural and urban Britain, and fertility rates among Scottish women, but the 1927 paper with McKendrick was his most influential contribution to science.

It contributed two things. First, Kermack and McKendrick described the interplay among three factors during an archetypal epidemic: the rate of infection, the rate of recovery, and the rate of death. They assumed that recovery from an attack conferred lifelong immunity (as it does, say, with measles) and outlined the dynamics in efficient English prose:

One (or more) infected person is introduced into a community of individuals, more or less susceptible to the disease in question. The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death. The chances of recovery or death vary from day to day during the course of his illness. The chances that the affected may convey infection to the unaffected are likewise dependent upon the stage of the sickness. As the epidemic spreads, the number of unaffected members of the community becomes reduced.

This sounds like calculus cloaked in words; and it is. Amid a dense flurry of mathematical manipulations, they derived a set of three differential equations describing the three classes of living individuals: the susceptible, the infected, and the recovered. During an epidemic, one class flows into another in a simple schema,
S → I →  R
, with mortalities falling out of the picture because they no longer belong to the population dynamic.
As susceptible individuals become exposed to the disease and infected, as infected individuals either recover (now with immunity) or disappear, the numerical size of each class changes at each moment in time. That’s why Kermack and McKendrick used differential calculus. Although I should have paid better attention to the stuff in high school, even I can understand (and so can you) that
dR/dt =
γ
I
merely means that the number of recovered individuals in the population, at a given moment, reflects the number of infected individuals times the average recovery rate. So much for
R
,
the “recovered” class. The equations for
S
(“susceptibles”) and
I
(“infected”) are likewise opaque but sensible. All this became known as an
SIR
model. It was a handy tool for thinking about infectious outbreaks, still widely used by disease theorists.

Eventually the epidemic ends.
Why
does it end? asked Kermack and McKendrick.

One of the most important problems in epidemiology
is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population.

They were leading their readers toward the second of those two possibilities: that an epidemic might cease because some subtle interplay among infectivity, mortality, and recovery (with immunity) has stifled it.

Their other major contribution was recognizing the existence of a fourth factor, a “threshold density” of the population of susceptible individuals. This threshold is the number of concentrated individuals such that, given certain rates of infectivity, recovery, and death, an epidemic can happen. So you have density, infectivity, mortality, and recovery—four factors interrelated as fundamentally as heat, tinder, spark, and fuel. Brought together in the critical measure of each, the critical balance, they produce fire: epidemic. Kermack and McKendrick’s equations calibrated the circumstances in which such a fire would ignite, would continue to burn, and would eventually smolder out.

One notable implication of their work was stated near the end: “
Small increases of the infectivity rate
may lead to large epidemics.” This quiet warning has echoed loudly ever since. It’s a cardinal truth, over which public health officials obsess each year during influenza season. Another implication was that epidemics don’t end because
all
the susceptible individuals are either dead or recovered. They end because susceptible individuals are no longer sufficiently dense within the population. W. H. Hamer had said so in 1906, remember? Ross had made the same point in 1916. But the paper by Kermack and McKendrick turned it into a working principle of mathematical epidemiology.

27

T
he second bit of landmark disease theory came from George MacDonald. He was another malaria researcher of mathematical bent (is it inevitable that so many of them be Scottish?), who worked in the tropics for years and eventually became director of the Ross Institute of Tropical Hygiene, in London, which had been founded decades earlier for Ronald Ross himself. MacDonald got some of his field experience in Ceylon (now Sri Lanka) during the late 1930s, just after a calamitous malaria epidemic there in 1934–1935, which sickened a third of the Ceylonese populace and killed eighty thousand. The severity of the Ceylon epidemic had been surprising because the disease was familiar, at least in parts of the island, recurring as modest annual outbreaks that mostly affected young children. What happened differently in 1934–1935 was that, after a handful of years with little malaria at all, a drought increased breeding habitat for mosquitoes (standing pools in the rivers, instead of flowing current), whose population then multiplied hugely, carrying malaria into areas where it had been long absent and where most people—especially the young children—possessed no acquired immunity. Back in London, fifteen and twenty years later, George MacDonald tried to understand how and why malaria exploded in occasional epidemics, using math as his method and Ceylon as a case in point.

That was just about the time, in the mid-1950s, when the World Health Organization began formulating a campaign to eradicate malaria globally, rather than just controlling or reducing it in one country and another. WHO’s vaunting ambition—total victory, no compromise—was partly inspired by the existence of a new weapon, the pesticide DDT, which seemed capable of exterminating mosquito populations and (unlike other insect poisons, which didn’t linger as lethal residue) keeping them dead. The other crucial element of WHO’s strategy was to eliminate malarial parasites from human hosts, also thoroughly, in order to break the human-mosquito-human cycle of infection. This would be achieved by treating every human case with malaria medicine, maintaining careful surveillance to detect any new or relapsing cases, and then treating those too, until the last parasite had been poisoned out of the last human bloodstream. That was the idea, anyway. George MacDonald’s writings were meant to clarify and assist the effort. One of them, published in WHO’s own
Bulletin
in 1956, was titled “Theory of the Eradication of Malaria.”

In an earlier paper, MacDonald had made the point that “
very small changes in the essential transmission factors
” of malaria in any given place could trigger an epidemic. This affirmed Kermack and McKendrick’s point about small increases in “infectivity” leading to large epidemics. But MacDonald was more specific. What were those essential transmission factors? He identified a whole list, including the density of mosquitoes relative to human density, the biting rate of the mosquitoes, the longevity of the mosquitoes, the number of days required for malarial parasites to complete a life cycle, and the number of days during which any infected human remains infectious to a mosquito. Some of these factors were known constants (a life cycle for
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.