Historical Aside on the Black Death and Plague in the 20th Century
The fascination with the Black Death, the catastrophic plague pandemic that swept through Europe in the mid-14th century, has not abated with the passage of time. Albert
Camus' The Plague, published in 1947, is one example, in a modern context. In the many accounts of the Black Death over the centuries, whether factual or romanticised, a vision has been conjured up of horrific carnage, wild debauchery, unbelievable acts of courage and altruism, and astonishing religious excesses.
The Black Death, principally bubonic plague, was caused by an organism (Bacillus pestis) and was transmitted by fleas, mainly from black rats, to man. It was generally fatal. The article by Langer (1964) gives a graphic description and some of the relevant statistics. The historical article by McEvedy (1988) discusses the pandemic's progress and surveys some of the current thinking on the periodic occurrences of bubonic plague. The plague was introduced to Italy in about December 1347, brought there by ship from the East where it had been raging for years. During the next few years it spread up through Europe at approximately 200-400 miles a year. About a quarter to a third of the population died and approximately 80% of those who contracted the disease died within 2-3 days. Figure 13.2 shows the geotemporal spread of the wavefront of the disease.
After the Black Death had passed, around 1350, a second major outbreak of plague appeared in Germany in 1356. From then on periodic outbreaks seemed to occur every few years although none of them were in the same class as regards severity as the Black Death epidemic of 1347. In Section 13.4 we shall describe an obvious extension to the simple model in this section which takes into account the partial recovery of the population after the passage of an epidemic wave. Including this results in periodic outbreaks, smaller ones, appearing behind the main front: see Figure 13.6 and Figure 13.7. Figures 13.9 and 13.10 in Section 13.5, which consider a three-species model for the spatial spread of a rabies epidemic, exhibit even more dramatic periodic epidemic waves which follow the initial outbreak. There we can estimate the period of the recurring outbreaks analytically.
There was a great variety of reactions to plague in mediaeval Europe and later (just as there is to plague today and the current AIDS epidemic).1 Groups of penitents, vigorously flagellating their half-naked bodies and preaching the coming of the end of the world, wandered about the countryside; some of the elegant and beautifully carved ivory handles of the flails of the richer flagellants still survive. Cures for the plague abounded during this period. One late 15th century cure, recently discovered in Westfalen-Lippe in northwest Germany, involved the following preparation. The tip of an almost hatched egg was cut off and the brood allowed to run out. The remaining egg yolk was mixed with raw saffron and the egg refilled and resealed with the shell pieces originally removed. The egg was afterwards fried until it turned brown. The recipe then called for the same amount of white mustard, some dill, a crane's beak and theriak (a popular quack medicine of the time). The mixture had to be swallowed by the victim who had to eat nothing more for 7 hours. There is no record of how effective this cure was!
The disease, of which there are three kinds, bubonic, pneumonic and septicemic, is caused by a bacillus carried primarily by fleas which are in turn carried by rats, mice and a host of other animals. Septicemic plague involves the bacilli multiplying extremely rapidly in the victim's blood and is almost invariably fatal (even now), whether treated or not; the victim usually dies very quickly and often suddenly. Septicemic plague often develops from the pneumonic form which is extremely contagious. There are descriptions of plague victims who suddenly sat down and simply keeled over dead. These could well have been septicemic cases who contracted it from the coughs of pneumonic victims. Children at the time of the Great Plague of London from 1664-1666, which peaked in 1665, used to sing the well-known English nursery rhyme
'Ring-a ring o'roses A pocket full of posies A-tishoo, A-tishoo We all fall down.'
1John Calvin, the scholar, theologian, unsurpassed killjoy and a man with a monumental ego and self-righteousness was convinced witches acting as agents of the devil brought it to Geneva where he was. He fled, terror stricken, from the epidemic and managed to survive (unfortunately). His baleful influence is still abundantly evident in the Scottish psyche and society even today and has, I am in no doubt, contributed to the massive emigration of Scots over the centuries to escape his depressing, deterministic and unforgiving view of the world.
which is believed to date from that period. Onions and garlic were held to the nose, in 'posies' or the bird-like masks of the physicians, to keep out the bad odours that were thought to be the cause of the disease.
There are considerably more data and information about the Great Plague of London in 1665 than are available about the Black Death. The people's reaction, however, seems not to have been dissimilar—fewer overt extreme penitents perhaps. The diarist Samuel Pepys describes the scene in my own university town of Oxford as one of 'lewd and dissolute behaviour'. Plus ca change...! Daniel Defoe's journal (1722) of the epidemic vividly conjures up a contemporary image and makes fascinating reading: 'It was then indeed, that man withered like the grass and that his brief earthly existence became a fleeting shadow. Contagion was rife in all our streets and so baleful were its effects, that the church-yards were not sufficiently capacious to receive the dead. It seemed for a while as though the brand of an avenging angel had been unloosed in judgment.'
There is a widely held belief that plague more or less ceased to be a problem after the Great Plague of London. This is far from the case, however, as clearly documented in the book by Gregg (1985). The last plague pandemic started in Yunnan in China about 1850 and only finished officially, according to the World Health Organisation, in 1959: more than 13 million deaths have been attributed to it, and it affected most parts of the world. The reported cases (and through ignorance or political expediency the figures must clearly be considered lower bounds) since 1959 makes it clear that plague epidemics are still with us. The thousands who died of it during the Vietnam war, particularly between 1965 and 1975, is a dramatic case to point.
Plague was brought by ship to the Northwest of America around 1900. About 200 deaths were recorded in the three-year San Francisco epidemic which started just after the earthquake in 1906. The article by Risse (1992) is specifically on this San Francisco epidemic. As a result of this epidemic, the western part of the U.S.A., particularly New Mexico, is now one of the two largest residual foci of plague (in mice and voles particularly) in the world—the other is in Russia. The plague bacillus has spread steadily eastwards from the west coast and in 1984 was found among animals in the midwest. The wavefront has moved on average about 35 miles a year. The disease is carried by a large number of native wild animals. Rats are by no means the sole carrier: it has been found in nearly 30 different mammals including, for example, squirrels, chipmunks, coyotes, prairie dogs, mice, voles, domestic pets and bats. The present complacency about the relatively small annual number of plague deaths is hardly justified. If, or rather when, plague reaches the east coast of the U.S.A. with its large urban areas, the potential for a serious epidemic will be considerable. New York, for example, has an estimated rat population of one rat per human; and mice—also effective disease carriers — probably number more. The prevailing lack of both concern and knowledge about the plague is dangerous. Plague symptoms are often not recognised or, at best, only belatedly diagnosed. Therefore the victim is free to expose a substantial number of people to the disease, particularly if it is pneumonic plague which is one of the most infectious diseases known.
To return now to our modelling, let us apply our simple epidemic model to the spread of the Black Death. We first have to estimate the relevant parameters, not a simple task with the paucity of hard facts about the social conditions of the time. Noble (1974) used such a model to investigate the spread of the plague and, after a study of the known facts, suggested approximate values for the parameters, some of which we use.
There were about 85,000,000 people in Europe in 1347 which gives a population density So ~ 50/mile2. It is particularly difficult to estimate the transmission coefficient r and the diffusion coefficient D. Let us suppose that the spread of news is governed by diffusion with a diffusion coefficient D. The time to cover a distance L miles purely by diffusion is then O (L2/D) years. Suppose, with the limited communications that existed at the time, that news and minor gossip, say, travelled at approximately 100 miles/year; this gives a value of D « 104 miles2/year. To transmit the disease the fleas have to jump from rats to humans and humans have to be close enough to infect other humans; this is reflected in the value for r. Noble (1974) estimated r to be 0.4 mile2/year. He took an average infectious period of two weeks (too long probably), which gives a mortality rate a ~ 15/year. These give X = a/(rS0) ~ 0.75. With the wavespeed given by (13.11) in terms of the model parameters, we then get the speed of propagation, V, of the plague as
Although this is somewhat lower than the speed of 200 to 400 miles/year, quoted by Langer (1964), it is not an unreasonable comparison in view of the gross estimates used for the unknown, and what are undeterminable, parameters.
Of course, such a model is extremely simple and does not take into account a number of factors, such as the nonuniformity in population density, the stochastic element and so on. Nevertheless it does indicate certain global features of the geographic spread of an epidemic. As we noted in Chapter 10, Section 10.2, Volume I the stochastic model studied by Raggett (1982) for the plague epidemic of 1665 to 1666 in the village of Eyam did not give as good comparison with the data as did the deterministic model. Stochastic elements, however, are more important in spatial models, particularly when the numbers involved are small.
Keeling and Gilligan (2000) have recently proposed an interesting new model for the spatiotemporal spread of the bubonic plague incidence (there are several thousand deaths each year).2 Plague is a zoonosis (a disease which spreads from animals to humans) and in many areas where it is prevalent rats are clearly implicated. Their model crucially incorporates the rat, as well as human, populations and includes stochasticity. They show that the disease can reside in rat subpopulations thereby letting the disease persist for many years. They discuss both deterministic and stochastic versions of their model and use a cellular automaton model to incorporate spatial stochasticity. From an analysis of their models they obtain, among other things, criteria for the spread in the human population in terms of the rat population. They use data on rodent populations from North America and use current estimates for the parameters.
2When I was visiting the Los Alamos National Laboratory in New Mexico in 1985 a 14-year-old boy in the neighbouring village died from getting infected while moving logs from a wood pile in which infected chipmunks had recently died of the disease. He contracted the septicemic form and died within three days.
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