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April 28 - May 26, 2024
Ronald Ross’s eventual discovery of the mosquito-mediated life cycle of malarial parasites, for which he won his Nobel Prize in 1902, is famous in the annals of disease research and I won’t retell it here.
Take measles. At first glance, it might seem nonmathematical. It’s caused by a paramyxovirus and shows itself as a respiratory infection, usually accompanied by a rash. It comes and it goes. But epidemiologists have recognized that, with measles virus, as with other pathogens, there’s a critical minimum size of the host population, below which it can’t persist indefinitely as an endemic, circulating infection. This is known as the critical community size (CCS),
In 1760, while holding a professorship at the University of Basel in Switzerland, Bernoulli produced a paper on smallpox, exploring the costs versus the benefits of universal immunization against that disease. His career was long and eclectic, encompassing mathematical work on a wide range of topics in physics, astronomy, and political economy, from the movement of fluids and the oscillation of strings to the measurement of risk and ideas about insurance. The smallpox study seems almost anomalous amid Bernoulli’s other interests, except that it also entailed the notion of calculating risk.
Almost a century later, the physician John Snow used statistical charts as well as maps to demonstrate which water sources (notably, the infamous Broad Street pump) were infecting the most people during London’s cholera outbreak of 1854.
He was right about something else, too: the difficulty of extirpating malaria “once and forever.”
Malaria is a vector-borne disease, yes, in that insects carry it from one host to another. But vectors are not hosts; they belong to a different ecological category from, say, reservoirs; and they experience the presence of the pathogen in a different way.
anyone who favors Intelligent Design in lieu of evolution might pause to wonder why God devoted so much of His intelligence to designing malarial parasites.
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.
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.
Although I should have paid better attention to the stuff in high school, even I can understand (and so can you) that dR/dt = γI 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.
“Small increases of the infectivity rate may lead to large epidemics.”
The 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?),
a drought increased breeding habitat for mosquitoes (standing pools in the rivers, instead of flowing current),
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.
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.
Robert S. Desowitz, who was a prominent parasitologist himself as well as a lively writer. “Institutions for malaria therapy rapidly proliferated throughout Europe and the technique was taken up in several centers in the United States. In this way, tens of thousands of syphilitics were saved from a sure and agonizing death”—saved by malaria.
That code is written in nucleotides, which are components of the DNA and RNA molecules. Each nucleotide consists of a nitrogenous base linked with a sugar molecule and one or more bits of phosphate. If DNA resembles a spiral staircase supported by two helical strands, those nitrogenous bases are the stair steps connecting the strands. There are four kinds of base in DNA—molecular components known as adenine, cytosine, guanine, and thymine, and abbreviated as A, C, G, and T, little pieces in the great game of genetic Scrabble.
In the RNA molecule, which serves for translating DNA into proteins (and has other roles, as we’ll see), a different piece called uracil substitutes for thymine, and the Scrabble pieces are therefore A, C, G, and U.
To say that “SARS got on a plane,” of course, is to commit metonymy and personification, both of which are forbidden to the authors of scientific journal articles but permissible to the likes of me.
seafood merchant was a man named Zhou Zuofeng. He holds the distinction of being the first “superspreader” of the SARS epidemic.
“Remember,” she told me, “all this time there are no diagnostic tests.” No tests, she meant, that detected presence or absence of the culpable infectious agent—because no one had yet identified that agent. “We are going purely based on epidemiology—whether there is contact with some of the source patients.” It was blind man’s bluff.
more precisely, like influenza at its worst. One form of influenza at its worst is the so-called bird flu, caused by a virus designated as H5N1,
infected by spillovers from domestic poultry. Eighteen doesn’t sound like a large number of patients; the fearful aspect was that six of those eighteen died. Health authorities had responded quickly, ordering the closure of live poultry markets and the destruction of every chicken in Hong Kong—amounting to 1.5 million doomed, squawking birds—followed by a seven-week hiatus for decontamination.
They were right, and the virus became known as SARS coronavirus, inelegantly abbreviated as SARS-CoV. It was the first coronavirus ever found to inflict serious illness upon humans.
People celebrated the end of the outbreak, but those best informed celebrated most guardedly. SARS-CoV wasn’t gone, it was only hiding. It could return.
Not even a surgical mask, let alone an N95. Um, why is that? I asked Aleksei. “I guess it’s like not wearing a seat belt,” he said. What he meant was that our exposure represented a calculated, acceptable risk. You fly to a strange country, you jump into a cab at the airport, you’re in a hurry, you don’t speak the language—and usually there’s no seat belt, right? Do you jump out and look for another cab? No, you proceed. You’ve got things to do. You might be killed on the way into town, true, but probably you won’t. Accepting that increment of risk is part of functioning within exigent
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What is it that makes this virus unusual? and What have we learned from the SARS experience? One thought that turns up in the latter sort is that “humankind has had a lucky escape.” The scenario could have been very much worse. SARS in 2003 was an outbreak, not a global pandemic.
(An ordinary bacterium differs from a virus in several obvious ways: It’s a cellular organism, not a subcellular particle; it’s much larger than a virus; it reproduces by fission, not by invading a cell and commandeering the cell’s machinery of genetic copying; and it can usually be killed by antibiotics.)
The parasitic mode of life is essentially similar to that of the predatory carnivores. It is just another method of obtaining food from the tissues of living animals,” though with parasites the consumption tends to be slower and more internalized within the prey. Small creatures eat bigger ones, generally from the inside out.
Burnet wrote, embodied a general truth about infectious disease. “It is a conflict between man and his parasites which, in a constant environment, would tend to result in a virtual equilibrium, a climax state, in which both species would survive indefinitely. Man, however, lives in an environment constantly being changed by his own activities, and few of his diseases have attained such an equilibrium.”
infection. It does follow logically—but erroneously. The syllogism would be sound, except that its first premise is oversimplified and misleading. “Deer ticks” of the species Ixodes scapularis do not draw their crucial sustenance from deer.
Any infectious disease is inherently an ecological system,” Ostfeld wrote.
Acarologists (tick biologists) have
Don’t look for romance in arachnoid sex.
Millbrook, New York, had taken their larval blood meal from (and therefore been infected by) either a white-footed mouse, a chipmunk, a short-tailed shrew, or a masked shrew. Those four hadn’t fed 90 percent of all blacklegged nymphs but, because of the differences in reservoir competence and grooming efficiency, they had fed 90 percent of those that became infected and dangerous to people.
Beyond helping the blacklegged tick (infected or uninfected) to survive, white-tailed deer are almost irrelevant to Lyme disease epidemiology. They don’t magnify the prevalence of infection in the forest. They don’t pass the spirochete to humans or to newly hatched ticks. They’re dead-end hosts, Ostfeld told me.
“I would feel a lot more comfortable,” Ostfeld answered, “if I knew that the landscape would support healthy populations of owls, foxes, hawks, weasels, squirrels of various kinds—the components of the community that could regulate mouse populations.” In other words, biological diversity.
We know that walking into a small woodlot,” he wrote, “is riskier than walking into a nearby large, extensive forest. We know that hiking in the oak woods two summers after a big acorn year is much riskier than hiking in those same woods after an acorn failure. We know that forests that house many kinds of mammals and birds are safer than those that support fewer kinds. We know that the more opossums and squirrels there are in the woods, the lower the risk of Lyme disease, and we suspect that the same is true of owls, hawks, and weasels.”
even in the age of antibiotics, bacteria can be sneaky and tough. These microbes remind us that you don’t have to be a virus to cause severe, intractable, mystifying outbreaks of zoonotic disease in the twenty-first century. Although it helps.
the study of what we now call by that name. It comes directly from the Latin virus, a term meaning “poison, sap of plants, slimy liquid.”
And bacteria weren’t quite so ineffable. They could be seen with a normal microscope. They could be cultured in a Petri dish (the invention of Julius Petri, Koch’s assistant) containing a nutrient-rich medium of agar.
A virus won’t grow in a medium of chemical nutrients because it can only replicate inside a living cell. In the technical parlance, it’s an “obligate intracellular parasite.”
But viruses aren’t all roundish. Some are cylindrical, some are stringy, some look like bad futuristic buildings or lunar landing modules. Whatever the shape, the interior volume is minuscule. The genomes packed within such small containers are correspondingly limited, ranging from 2,000 nucleotides up to about 1.2 million. The genome of a mouse, by contrast, is about 3 billion nucleotides. It takes three nucleotide bases to specify an amino acid and on average about 250 amino acids to make a protein (though some proteins are much larger). Making proteins is what genes do; everything else in a
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Viruses face four basic challenges: how to get from one host to another, how to penetrate a cell within that host, how to commandeer the cell’s equipment and resources for producing multiple copies of itself, and how to get back out—out of the cell, out of the host, on to the next. A virus’s structure and genetic capabilities are shaped parsimoniously to those tasks.
Macfarlane Burnet, defined a virus as “a piece of bad news wrapped up in a protein
The protein wrap is known as a capsid. The capsid serves two purposes: It protects the viral innards when they need protection and it helps the virus lever its way into cells.
Herpesviruses, poxviruses, and papillomaviruses contain DNA; so do half a dozen viral families you’ve never heard of, such as the iridoviruses, the baculoviruses, and the hepadnaviruses (one of which causes hepatitis B). Others, including filoviruses, retroviruses (most notoriously, HIV-1), coronaviruses (SARS-CoV), and the families encompassing measles, mumps, Hendra, Nipah, yellow fever, dengue, West Nile, rabies, Machupo, Junin, Lassa, chikungunya, all the hantaviruses, all the influenzas, and the common cold viruses, store their genetic information in the form of RNA.
(adenine linking only with thymine, cytosine only with guanine), it generally repairs mistakes in the placement of bases as it replicates itself. This repair work is performed by DNA polymerase, the enzyme that helps catalyze construction of new DNA from single strands. If an adenine is mistakenly set in place to become linked with a guanine (not its correct partner), the polymerase recognizes that mistake, backtracks by one pair, fixes the mismatch, and then moves on. So the rate of mutation in most DNA viruses is relatively low. RNA viruses, coded by a single-strand molecule with no such
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To every rule, an exception. But we’re going to ignore those minor anomalies because this stuff is already complicated enough.) The basic point is so important I’ll repeat it: RNA viruses mutate profligately.