from an eminent mentor there, Ross himself saw the “Laveran bodies” in malarial blood and was converted to Laveran’s idea, so far as it went.
Laveran had detected the important truth that malaria is caused by microbes, not by bad air. But that still left unexplained the wider matters of how these microbes reproduced in a human body, and how they passed from one host to another. Were they carried and ingested in water, like the germ causing cholera? Or might they be transmitted in the bite of an insect?
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. It’s a complicated story, both because the life cycle of the parasites is so amazingly complex and because Ross, himself a complicated man, had so many influences, competitors, enemies, wrong ideas as well as right ones, and distracting disgruntlements. Two salient points are enough to suggest the connections of that story to our subject, zoonoses. First, Ross delineated the life history of malarial parasites not as he found them infecting humans but as he found them infecting birds. Bird malaria is distinct from human malaria but it served as his great analogy. Second, he came to see the disease as a subject for applied mathematics.
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Numbers can be an important aspect of understanding infectious disease. 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), an important parameter in disease dynamics. The critical community size for measles seems to be somewhere around five hundred thousand people. That number reflects characteristics specific to the disease, such as the transmission efficiency of the virus, its virulence (as measured by the case fatality rate), and the fact that one-time exposure confers lifelong immunity. Any isolated community of less than a half million people may be struck by measles occasionally, but in a relatively short time the virus will die out. Why? Because it has consumed its opportunities among susceptible hosts. The adults and older children in the population are nearly all immune, having been previously exposed, and the number of babies born each year is insufficient to allow the virus a permanent circulating presence. When the population exceeds five hundred thousand, on the other hand, there will be a sufficient and continuing supply of vulnerable newborns.
Another crucial aspect of measles is that the virus is not zoonotic. If it were—if it circulated also in animals living near or among human communities—then the question of critical community size would be moot. There wouldn’t be any necessary minimum size of the human population, because the virus could always remain present, nearby, in that other source. But bear in mind that measles, though it doesn’t circulate in nonhuman animal populations, is closely related to viruses that do. Measles belongs to the genus Morbillivirus, which includes canine distemper and rinderpest; its family, Paramyxoviridae, encompasses also Hendra and Nipah. Although measles doesn’t often pass between humans and other animals, its evolutionary lineage speaks of such passage sometime in the past.
Whooping cough, to take another example, has a critical community size that differs slightly from the measles number because it’s a different disease, caused by a microbe with different characteristics: different transmission efficiency, different virulence, different period of infectivity, et cetera. For whooping cough, the CCS seems to be more like two hundred thousand people. Such considerations have become grist for a lot of fancy ecological mathematics.
Daniel Bernoulli, a Dutch-born mathematician from a family of mathematicians, was arguably the first person to apply mathematical analysis to disease dynamics, long before the germ theories of disease (there was a gaggle, not just one) became widely accepted. 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