Previously this week I spotted a mildly interesting news item.

BBC reports that …

Rats were not to blame for the spread of plague during the Black Death, according to a study.

The rodents and their fleas were thought to have spread a series of outbreaks in 14th-19th Century Europe.

But a team from the universities of Oslo and Ferrara now says the first, the Black Death, can be “largely ascribed to human fleas and body lice”.

Then I spotted it again on HN, and noticed that one of the authors participated in the discussion.

Hey, look, it’s Bayesian! So I thought to take a look at the study itself (maybe I can learn something form it?!)

### High-level summary

The reference is:

Katharine R. Dean, Fabienne Krauer, Lars Walløe, Ole Christian Lingjærde, Barbara Bramanti, Nils Chr. Stenseth, and Boris V. Schmid,
“Human ectoparasites and the spread of plague in Europe during the Second Pandemic”
link
doi: 10.1073/pnas.1715640115

The paper can be summarized surprisingly shortly: (Surprising to me, that is.)

The authors specify three deterministic, dynamic transmission models for bubonic plague: one where the transmission vector is assumed to be human ectoparasites (lice, fleas), another model with direct human-to-human transmission (pneumonic plague), and third model with the rat-flea-humans transmission model familiar from school textbooks. (Oh, by the way, “dynamic model” sounds very … dynamic, but here it means a model described system described by a set of time-dependent differential equations.)

The parameters of each model are either fixed to parameter estimates found from the literature (“probability of recovery from bubonic plague”, “natural lice growth rate”, etc) or set an uniform prior over some interval when point estimate wasn’t available (such as “transmission rate for bubonic plague from mildly infectious humans to body lice”), meant to capture the uncertainty. Then the model is fitted (PyMC2) to the death toll records from nine plague outbreaks in medieval Europe (the observed mortality data is assumed to follow Poisson distribution, where the mean number of deaths over time period $\lambda$ is given by the deterministic model.) The authors observe that in seven cases out of nine, the human ectoparasite model achieves the best fit to data.

Example Python code was made available by the authors and can be found behind the link. (Everybody loves IPy/Jupyter notebooks these days, except me?)

But what to think about the paper? In general, I think it’s an example of very exciting application of Bayesian modeling. But at the same time, its importance as an explanation epidemiology of bubonic plague hinges on the correctness of the underlying biological models. And those biological details are exactly the ones I don’t really feel qualified to answer. Do the specified models make sense? What other modeling choices there would be? Could one specify the rats-to-people model in some other way that would achieve a better fit? How sensitive the models are to change of the fixed parameter estimates? So many questions! Only thing I think I can say is that it looks plausible, but not conclusive either.

The authors also note that even at their theoretical best, the models they use can capture only part of the disease epidemiology. For example, some recorded plague epidemics have two mortality peaks, not explained by the models studied.

### Post scriptum. Popular summary by one of the authors

Only after writing the above piece, I noticed that one of the authors (Boris V. Schmid) had written much better popular science summary on his Medium blog with more detail on the historical background of Black Death. This is what he thinks is the main giveaway of the study at hand:

Until now, the hypothesis of human ectoparasite transmission has been regarded as highly speculative and was supported only by indirect evidence, like different overall mortality levels between the Second and Third Pandemics, the scarcity of rat bones in archeological digs, and the presence of ancient DNA from louse-borne diseases in a plague victim (Leulmi et al, 2014). While modeling studies are not necessarily decisive, they do offer powerful insights into disease processes where experimental, historical, and archaeological information is lacking, and can serve as a stepping stone for other disciplines to build upon. With our results, we hope to shift some attention away from the rat transmission paradigm and open up new avenues for research (experimental, epidemiological and historical) into human ectoparasites as important vectors in past and current plague epidemics.