The analysis of historic and recent records of plague epidemics have brought into relief surprising discrepancies between the characteristics of past and present epidemics that we had so far been all attributing to plague. For example, Mark Welford and Brian Bossak have shown that while current laboratory-confirmed cases generally occur between November and April, Medieval Black Death epidemics recurrently burst between April and October. Have we been wrongly attributing the Black Death epidemics to the bubonic and pneumonic plagues? This question remains open, and we are simply going to illustrate here how mechanistic models could be used to provide further insight into the characteristics of present and historic epidemics.
We will be looking at two time series of 1665 epidemics in the UK, each indicating the monthly number of deaths caused by plague in London and Eyam. Contrasting these two cases is not only interesting due to the population size difference between London and Eyam, that had respectively 460000 and 350 inhabitants at the beginning of the epidemics, but also due to the peculiar story of the city of Eyam. As some villagers started to die from plague, the clergyman William Monpesson decided to isolate the village in order to protect the neighbouring cities of Northern England. During one year, Eyam lived in quarantine. Food was cautiously supplied so that villagers did not starve. Yet, at the end of the epidemic 250 people had died.
This story sheds a particular light on the following time series, that can be found in the Bills of Mortality. Since 1932, these records had been filled by English doctors in order to monitor the number of deaths due to tuberculosis, small pox, measles, French pox, and plague:
To analyse this dataset we use a simple model in which individuals are either infected with plague or
susceptible to become infected. Seasonal forcing is accounted for, which timing and amplitude are being estimated.
At last, we make no assumption on the type of plague involved in this epidemic, allowing the life expectancy after
infection to lie between one and seven days (respectively corresponding to pneumonic and bubonic plague).
The resulting estimates of the transmission potential of plague in each city, as well as life expectancy with
plague, are the following:
These results provide information that could not have been inferred from direct observation of the time series of deaths in each city. First, they suggest that the isolation and living conditions in Eyam lead to a higher transmissibility of the disease. Furthermore, life expectancy after infection appears to be close to one week, suggesting that this epidemic was a bubonic plague rather than a pneumonic plague. The latter seems to be confirmed by historical records.
For the sake of transparency, and to foster further explorations of this problem and the data provided by Mark Welford and Brian Bossak, this repository provides the means to easily reproduce the presented results. It relies on the library of inference methods developed in collaboration with Sébastien Ballesteros as part the the PLOM.IO project.
Data is contained in the data folder, in the csv format. Additionally, the folder SI_seas contains json files that define a model and link it to the data, following the PLOM.IO grammar. To generate the code and play with the model yourself, simply install the package, and compile the model with:
plom build -t map.json --local
The joint posterior density of parameters can be explored with:
plom pipe map.json | ./pmcmc --full -J 2000 -N 8 -a 0.98 -M 20000
Which will create a trace_0.csv file.