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

The Black Death in Hereford, England: A demographic analysis of the Cathedral 14th-century plague mass graves and associated parish cemetery

OBJECTIVES

This study explores the paleoepidemiology of the Black Death (1348-52 AD) mass graves from Hereford, England, via osteological analysis. Hereford plague mortality is evaluated in the local context of the medieval city and examined alongside other Black Death burials.

METHODS

The Hereford Cathedral site includes mass graves relating to the Black Death and a 12th-16th century parish cemetery. In total, 177 adult skeletons were analyzed macroscopically: 73 from the mass graves and 104 from the parish cemetery. Skeletal age-at-death was assessed using transition analysis, and sex and stress markers were analyzed.

RESULTS

The age-at-death distributions for the mass graves and parish cemetery were significantly different (p = 0.0496). Within the mass graves, young adults (15-24 years) were substantially over-represented, and mortality peaked at 25-34 years. From 35 years of age onwards, there was little variation in the mortality profiles for the mass graves and parish cemetery. Males and females had similar representation across burial types. Linear enamel hypoplasia was more prevalent within the mass graves (p = 0.0340) whereas cribra orbitalia and tibial periostitis were underrepresented.

CONCLUSIONS

Mortality within the Hereford mass graves peaked at a slightly older age than is seen within plague burials from London, but the overall profiles are similar. This demonstrates that young adults were disproportionately at risk of dying from plague compared with other age groups. Our findings regarding stress markers may indicate that enamel hypoplasia is more strongly associated with vulnerability to plague than cribra orbitalia or tibial periostitis.

Discrete Models in Epidemiology: New Contagion Probability Functions Based on Real Data Behavior

Mathematical modeling is a tool used for understanding diseases dynamics. The discrete-time model is an especial case in modeling that satisfactorily describes the epidemiological dynamics because of the discrete nature of the real data. However, discrete models reduce their descriptive and fitting potential because of assuming a homogeneous population. Thus, in this paper, we proposed contagion probability functions according to two infection paradigms that consider factors associated with transmission dynamics. For example, we introduced probabilities of establishing an infectious interaction, the number of contacts with infectious and the level of connectivity or social distance within populations. Through the probabilities design, we overcame the homogeneity assumption. Also, we evaluated the proposed probabilities through their introduction into discrete-time models for two diseases and different study zones with real data, COVID-19 for Germany and South Korea, and dengue for Colombia. Also, we described the oscillatory dynamics for the last one using the contagion probabilities alongside parameters with a biological sense. Finally, we highlight the implementation of the proposed probabilities would improve the simulation of the public policy effect of control strategies over an infectious disease outbreak.

Differential word expression analyses highlight plague dynamics during the second pandemic

Research on the second plague pandemic that swept over Europe from the fourteenth to nineteenth centuries mainly relies on the exegesis of contemporary texts and is prone to interpretive bias. By leveraging certain bioinformatic tools routinely used in biology, we developed a quantitative lexicography of 32 texts describing two major plague outbreaks, using contemporary plague-unrelated texts as negative controls. Nested, network and category analyses of a 207-word pan-lexicome, comprising overrepresented terms in plague-related texts, indicated that 'buboes' and 'carbuncles' are words that were significantly associated with the plague and signalled an ectoparasite-borne plague. Moreover, plague-related words were associated with the terms 'merchandise', 'movable', 'tatters', 'bed' and 'clothes'. Analysing ancient texts using the method reported in this paper can certify plague-related historical records and indicate the particularities of each plague outbreak, which can inform on the potential sources for the causative Yersinia pestis.

The influence of temperature on the seasonality of historical plague outbreaks

Modern plague outbreaks exhibit a distinct seasonal pattern. By contrast, the seasonality of historical outbreaks and its drivers has not been studied systematically. Here, we investigate the seasonal pattern, the epidemic peak timing and growth rates, and the association with latitude, temperature, and precipitation using a large, novel dataset of plague- and all-cause mortality during the Second Pandemic in Europe and the Mediterranean. We show that epidemic peak timing followed a latitudinal gradient, with mean annual temperature negatively associated with peak timing. Based on modern temperature data, the predicted epidemic growth of all outbreaks was positive between 11.7°C and 21.5°C with a maximum around 17.3°C. Hence, our study provides evidence that the growth of plague epidemics across the whole study region depended on similar absolute temperature thresholds. Here, we present a systematic analysis of the seasonality of historical plague in the Northern Hemisphere, and we show consistent evidence for a temperature-related process influencing the epidemic peak timing and growth rates of plague epidemics.

Estimating the basic reproduction number for the 2015 bubonic plague outbreak in Nyimba district of Eastern Zambia

BACKGROUND

Plague is a re-emerging flea-borne infectious disease of global importance and in recent years, Zambia has periodically experienced increased incidence of outbreaks of this disease. However, there are currently no studies in the country that provide a quantitative assessment of the ability of the disease to spread during these outbreaks. This limits our understanding of the epidemiology of the disease especially for planning and implementing quantifiable and cost-effective control measures. To fill this gap, the basic reproduction number, R0, for bubonic plague was estimated in this study, using data from the 2015 Nyimba district outbreak, in the Eastern province of Zambia. R0 is the average number of secondary infections arising from a single infectious individual during their infectious period in an entirely susceptible population.

METHODOLOGY/PRINCIPAL FINDINGS

Secondary epidemic data for the most recent 2015 Nyimba district bubonic plague outbreak in Zambia was analyzed. R0 was estimated as a function of the average epidemic doubling time based on the initial exponential growth rate of the outbreak and the average infectious period for bubonic plague. R0 was estimated to range between 1.5599 [95% CI: 1.382-1.7378] and 1.9332 [95% CI: 1.6366-2.2297], with average of 1.7465 [95% CI: 1.5093-1.9838]. Further, an SIR deterministic mathematical model was derived for this infection and this estimated R0 to be between 1.4 to 1.5, which was within the range estimated above.

CONCLUSIONS/SIGNIFICANCE

This estimated R0 for bubonic plague is an indication that each bubonic plague case can typically give rise to almost two new cases during these outbreaks. This R0 estimate can now be used to quantitatively analyze and plan measurable interventions against future plague outbreaks in Zambia.

A digital reconstruction of the 1630-1631 large plague outbreak in Venice

The plague, an infectious disease caused by the bacterium Yersinia pestis, is widely considered to be responsible for the most devastating and deadly pandemics in human history. Starting with the infamous Black Death, plague outbreaks are estimated to have killed around 100 million people over multiple centuries, with local mortality rates as high as 60%. However, detailed pictures of the disease dynamics of these outbreaks centuries ago remain scarce, mainly due to the lack of high-quality historical data in digital form. Here, we present an analysis of the 1630-1631 plague outbreak in the city of Venice, using newly collected daily death records. We identify the presence of a two-peak pattern, for which we present two possible explanations based on computational models of disease dynamics. Systematically digitized historical records like the ones presented here promise to enrich our understanding of historical phenomena of enduring importance. This work contributes to the recently renewed interdisciplinary foray into the epidemiological and societal impact of pre-modern epidemics.

A forensic evaluation of plague - a re-emerging infectious disease with biowarfare potential

Plague is an acute infectious disease caused by the gram-negative cocco-bacillus Yersinia pestis. It has been responsible for 200 million deaths throughout history with three major pandemics. There are three forms: bubonic, septicaemic and pneumonic, each carrying a significant mortality rate. The usual transmission is from fleas carried by rodents. Recently, it has been listed as one of the reemerging infectious diseases globally, with a potential use in bioterrorism. At autopsy there may be lymphadenopathy, fulminant pneumonia or diffuse interstitial pneumonitis. However any organ may be affected with myocarditis, meningitis, pharyngitis and hepatic and splenic necrosis. The lethality of plague with the resurgence in numbers of cases, development of antibiotic resistance, recent occurrence in urban areas and the lack of a vaccine make it a disease not to be missed in the mortuary.

Simple multi-scale modeling of the transmission dynamics of the 1905 plague epidemic in Bombay

The first few disease generations of an infectious disease outbreak is the most critical phase to implement control interventions. The lack of accurate data and information during the early transmission phase hinders the application of complex compartmental models to make predictions and forecasts about important epidemic quantities. Thus, simpler models are often times better tools to understand the early dynamics of an outbreak particularly in the context of limited data. In this paper we mechanistically derive and fit a family of logistic models to spatial-temporal data of the 1905 plague epidemic in Bombay, India. We systematically compare parameter estimates, reproduction numbers, model fit, and short-term forecasts across models at different spatial resolutions. At the same time, we also assess the presence of sub-exponential growth dynamics at different spatial scales and investigate the role of spatial structure and data resolution (district level data and city level data) using simple structured models. Our results for the 1905 plague epidemic in Bombay indicates that it is possible for the growth of an epidemic in the early phase to be sub-exponential at sub-city level, while maintaining near exponential growth at an aggregated city level. We also show that the rate of movement between districts can have a significant effect on the final epidemic size.

Model-based analysis of an outbreak of bubonic plague in Cairo in 1801

Bubonic plague has caused three deadly pandemics in human history: from the mid-sixth to mid-eighth century, from the mid-fourteenth to the mid-eighteenth century and from the end of the nineteenth until the mid-twentieth century. Between the second and the third pandemics, plague was causing sporadic outbreaks in only a few countries in the Middle East, including Egypt. Little is known about this historical phase of plague, even though it represents the temporal, geographical and phylogenetic transition between the second and third pandemics. Here we analysed in detail an outbreak of plague that took place in Cairo in 1801, and for which epidemiological data are uniquely available thanks to the presence of medical officers accompanying the Napoleonic expedition into Egypt at that time. We propose a new stochastic model describing how bubonic plague outbreaks unfold in both rat and human populations, and perform Bayesian inference under this model using a particle Markov chain Monte Carlo. Rat carcasses were estimated to be infectious for approximately 4 days after death, which is in good agreement with local observations on the survival of infectious rat fleas. The estimated transmission rate between rats implies a basic reproduction number R₀ of approximately 3, causing the collapse of the rat population in approximately 100 days. Simultaneously, the force of infection exerted by each infected rat carcass onto the human population increases progressively by more than an order of magnitude. We also considered human-to-human transmission via pneumonic plague or human specific vectors, but found this route to account for only a small fraction of cases and to be significantly below the threshold required to sustain an outbreak.

Human ectoparasites and the spread of plague in Europe during the Second Pandemic

Plague, caused by the bacterium Yersinia pestis, can spread through human populations by multiple transmission pathways. Today, most human plague cases are bubonic, caused by spillover of infected fleas from rodent epizootics, or pneumonic, caused by inhalation of infectious droplets. However, little is known about the historical spread of plague in Europe during the Second Pandemic (14-19th centuries), including the Black Death, which led to high mortality and recurrent epidemics for hundreds of years. Several studies have suggested that human ectoparasite vectors, such as human fleas (Pulex irritans) or body lice (Pediculus humanus humanus), caused the rapidly spreading epidemics. Here, we describe a compartmental model for plague transmission by a human ectoparasite vector. Using Bayesian inference, we found that this model fits mortality curves from nine outbreaks in Europe better than models for pneumonic or rodent transmission. Our results support that human ectoparasites were primary vectors for plague during the Second Pandemic, including the Black Death (1346-1353), ultimately challenging the assumption that plague in Europe was predominantly spread by rats.

Subspace identification for a stochastic model of plague

In this paper, a stochastic model of plague is first studied by subspace identification. First, the discrete model of plague is obtained based on the classical model. The corresponding stochastic model is proposed for the existence of stochastic disturbances. Second, for the model, the parameter matrices and noise intensity are obtained. Finally, the simulations of the model show that the subspace identification is more precise than least square method.

Global parasite and Rattus rodent invasions: The consequences for rodent-borne diseases

We summarize the current knowledge on parasitism-related invasion processes of the globally invasive Rattus lineages, originating from Asia, and how these invasions have impacted the local epidemiology of rodent-borne diseases. Parasites play an important role in the invasion processes and successes of their hosts through multiple biological mechanisms such as "parasite release," "immunocompetence advantage," "biotic resistance" and "novel weapon." Parasites may also greatly increase the impact of invasions by spillover of parasites and other pathogens, introduced with invasive hosts, into new hosts, potentially leading to novel emerging diseases. Another potential impact is the ability of the invader to amplify local parasites by spillback. In both cases, local fauna and humans may be exposed to new health risks, which may decrease biodiversity and potentially cause increases in human morbidity and mortality. Here we review the current knowledge on these processes and propose some research priorities.

The model of Kermack and McKendrick for the plague epidemic in Bombay and the type reproduction number with seasonality

The figure showing how the model of Kermack and McKendrick fits the data from the 1906 plague epidemic in Bombay is the most reproduced figure in books discussing mathematical epidemiology. In this paper we show that the assumption of constant parameters in the model leads to quite unrealistic numerical values for these parameters. Moreover the reports published at the time show that plague epidemics in Bombay occurred in fact with a remarkable seasonal pattern every year since 1897 and at least until 1911. So the 1906 epidemic is clearly not a good example of epidemic stopping because the number of susceptible humans has decreased under a threshold, as suggested by Kermack and McKendrick, but an example of epidemic driven by seasonality. We present a seasonal model for the plague in Bombay and compute the type reproduction numbers associated with rats and fleas, thereby extending to periodic models the notion introduced by Roberts and Heesterbeek.