Modelling the black death. A historical case study and implications for the epidemiology of bubonic plague

We analysed a plague outbreak in the mining town of Freiberg in Saxony which started in May 1613 and ended in February 1614. This epidemic was selected for study because of the high quality of contemporary sources. It was possible to identify 1400 individual victims meaning that more than 10% of the population of the city perished. The outbreak was modelled by 9 differential equations describing flea, rat, and human populations. This resulted in a close fit to the historical records of this outbreak. An interesting implication of the model is that the introduction of even a small number of immune rats into an otherwise unchanged setting results in an abortive outbreak with very few human victims. Hence, the percentage of immune rats directly influences the magnitude of a human epidemic by diverting search activities of the fleas. Thus, we conclude that the spread of Rattus norvegicus, which might acquire partial herd immunity by exposure to soil- or water-borne Yersinia species due to its preference for wet habitats, contributed to the disappearance of Black Death epidemics from Europe in the 18th century. In order to prove whether or not the parameter values obtained by fitting a given outbreak are also applicable to other cases, we modelled the plague outbreak in Bombay 1905/06 using the same parameter values except for the number of humans as well as of immune and susceptible rats.