## Introduction

Plague is initiated by the flea-borne bacterium Yersinia pestis, which circulates mainly on rodents and other mammal hosts through the rodent’s associated fleas1,2. Normally, the bloodsucking fleas acquire Yersinia pestis from an infected rodent. The bacterium will quickly multiply and cluster, leading to the blockage of the alimentary canal in the fleas’ guts3. When the infected flea jumps onto another mammal, preferably rodents, it will transmit the bacteria to the new host by regurgitating the clotted blood from the blockage of the alimentary canal4. If an infected flea attempts to feed on a human, it will transmit Yersinia pestis to the human and lead to human plague in the form of bubonic plague or pulmonary plague. Traditional thought suggested that the clustering of Yersinia pestis rarely happened on human fleas5. Yet, recent evidence revealed that not only rodent fleas (Xenopsylla cheopis as a classic example) are to blame for plague transmission, human fleas (Pulex irritans) and cat fleas (Ctenocephalides felis) are also likely to play a role in disseminating Yersinia pestis 6,7. Furthermore, laboratory results illustrated the experimental possibility of oral route transmission of plague8 and epidemiological records suggested plague infection through consumption of contaminated meat9,10.

Despite improvements in sanitation and medical advancements in the course of human history, plague remains a major threat to human beings11,12. Over the past few decades, thousands of cases of human plague have occurred around the world, particularly in Africa13. Some researchers suggested that plague may reign over our planet again when global climate change makes some places on earth become wetter and hotter14,15,16. Considering the widespread wildlife reservoirs of plague foci, together with the quick spread, rapid clinical course, inherent communicability, and high mortality rate of plague, the risk of plague outbreak should never be underestimated, although the number of human plague cases is relatively low compared to other infectious diseases at present17. Flashing back in history, plague caused three great pandemics, in which 200 million people perished18. Given the nature of plague and its notorious history, the international community should be more prepared for the re-emergence of plague. Ironically, remarkably little research has been done to elucidate how plague spread through metastatic spatial domains and the mechanism behind its distribution.

Other scholars have long identified the influence of trade routes on plague transmission in historical Europe20,23,29,30. Yet, no scientific consensus could be reached concerning the coherence of plague outbreaks and major trade route patterns. Here, we based on our statistical results to prove that there would be more plague outbreaks when a city is closer to the major trade routes. Moreover, the evidence found in our investigation of the plague/trade-port relationship did not indicate any sign of permanent plague reservoirs in the inland areas of Europe in history. Plague was imported from trade ports or it originated from somewhere linked to the maritime trading system. Sporadic plague outbreak was used as an indicator to show the different roles of trade routes and navigable rivers in plague transmission. A specific case study of Germany indicated that a local trade route was more important in distributing plague outbreak. Altogether, the results allowed us to propose a potential plague transmission mechanism.

## Results

We combined records of 6,656 plague outbreak cases in historical Europe and North Africa and the trade route database that geo-referenced the major overland and maritime trade routes during the early modern period (Fig. 1). To examine whether trade routes were related to the plague outbreak patterns during our study period, we started by checking whether plague hotspots were also key trade nodes. According to a recent study by Schmid et al.30, there was never any permanent plague reservoir in pre-industrial Europe. This implied that a plague outbreak at any given place in our study area was transmitted from a nearby outbreak. If human movements and the circulation of goods provided an ideal channel for the spread of plague, a city’s proximity to key trade nodes would determine its likelihood to become a plague hotspot.

The top 20 cities with the highest year count of plague outbreaks between AD1347 and 1760 are listed in Table 1. Thirteen of these cities were key trade nodes that linked trade routes together. These cities were geographically dispersed and spread in seven countries. As stated by Vogler et al.31, maritime ports were common plague outbreak centers when “plague ships” introduced infected rodent hosts and flea vectors to the cities. In addition, even though half of the trade nodes as documented in our dataset are port cities, only six port cities (in six countries) are listed in Table 1. The same result was also obtained with a sensitivity test (Table S2). Briefly, plague hotspots were mostly trade nodes. Yet, there seemed to be no evidence to support that those hotspots were necessarily port cities. We dissimilated this pattern by searching for the relationship between plague outbreak and its distance to trade route and trade port.

The OLS estimates revealed that distance to trade route has a high explanatory power to the distribution of plague outbreak. Despite its large sample size (n = 6,656), the R2 ranged from 0.41 to 0.44 in Models 2 to 6. The negativity of the association implies that cities closer to trade routes were more vulnerable to plague reoccurrence. On the other hand, being further away from trade routes was a good way to escape from plague.

We performed several sensitivity tests to further check the robustness of our OLS regression results (Table S3). It was shown that the relationship between plague outbreak and trade route was highly significant and remained negative in different temporal domains of our study period (AD 1347–1449, AD1450–1549, AD1550–1649, and AD1650–1760). In addition, the relationship was robust in our different specification of spatial domains, in which the cases in Russia and Africa were excluded, or only the cases in continental Europe and the six major plague outbreak countries were included (see SI for more details). The above results implied that the pattern of plague outbreak was determined by the trade route patterns for the entire study area, which was consistent over the study period. Hence, the relationship should be independent of cultural, demographic, economic factors or the possible spatial bias of plague database as suggested by Alfani37. Otherwise, the relationship over different regions and time periods should differ.

However, there must be certain ways for animal hosts to cause these sporadic outbreaks scattered around the European continent. It might be attributable to some less active transportation routes (e.g., navigable rivers) that connected these sporadic cases with the plague hotspots. We calculated the correlation between distance to the closest navigable river and plague outbreak for these sporadic cases (Table S7). We found that although navigable rivers were not as capable as major trade routes in influencing the total plague transmission (Table S8), they did account for the pattern of sporadic plague distribution in historical Europe (p < 0.005; F = 6.13). There were more outbreaks of plague in those cities located closer to the navigable rivers. The result was also verified by robustness checks in various geographical specifications. It confirmed that local river channels, instead of major trade routes, were more significant in determining the distribution of sporadic plague outbreak cases in early modern Europe.

## Discussions

Prior to the Industrial Revolution, long distance human movement was mainly confined to the trading of goods along certain overland trade routes, navigable rivers, and maritime trade routes43. Plague was spread primarily by its rodent host or occasionally vectorized by other animal hosts. However, these hosts did not move across Europe themselves, but were transported by humans along the major trade routes. By combing data from historical trade routes and plague records, we found that the geographic pattern of plague was determined by major trade routes in early modern Europe.

There were five key findings in our statistical results. First, places closer to trade routes were more prone to plague outbreak and thus, plague reoccurrence. Second, plague was repeatedly introduced to several key trade ports and spread further inland in early modern Europe. Third, we found no sign of a permanent plague reservoir according to the distribution of plague outbreak. Forth, localized river navigation systems instead of trade routes accounted for the geographic distribution of sporadic plague outbreaks. Fifth, the case study of Germany suggested that local trade routes could be a significant explanatory factor to plague transmission. Based on these findings, we proposed a hypothetical corollary for plague transmission in historical Europe (Fig. 4).

It might be argued that maritime trade routes were not the sole way for plague to conquer the European continent. Plague might be repeatedly introduced to Europe through the overland trade routes such as the Silk Road. In such case, a plague pandemic would transfer from inland to port and then it was exported to other places of Europe. However, this plague transmission pathway could not be supported by our statistical results. Our robustness check showed that plague was either imported to Europe by maritime trade routes or a specific trade port was developed as a plague reservoir.

According to our results, major trade routes did not account for sporadic plague cases. In fact, the imperative role of navigable rivers in connecting cities after the medieval era has been mentioned by Edwards and Hindle45 and Jones46 and is also highlighted by our statistical analyses in spreading plague. Inland waterways provided further penetration for the contagion from various major trade routes to the hinterland. Our results proved that the further away from navigable rivers, the number of plague outbreak dropped in a statistically significant manner. Certain contagions might have left the major trade routes and spread to other settlements through inland waterways. Although these sporadic cases seemed to be randomly distributed, they were indeed anchored with trade routes.

The above explanation might not totally account for the pattern of sporadic plague outbreak in historical Europe as indicated by the low F and R2 values in the statistical analysis (F = 6.13, R2 = 0.0748, Table S7). Certain sporadic cases in our database would be attributable to other factors such as war or undocumented localized trade/communication routes. Also, sporadic events which cannot be addressed by our research methods might actually cluster in certain temporal and spatial scales. However, when we looked at long distance travel or major carriers of plague in a long-temporal and large-spatial perspective, major trade route largely accounts for the distribution of plague outbreaks.

Ideally, we would prefer to test our model with local trade route at high spatial resolution in Europe against plague distribution. Unfortunately, these data are unavailable at the moment. Given this shortcoming, we were only able to issue a case study of Germany as evidence of the role of local trade routes in plague transmission. The result further validated the possible linkage between trade route and plague recurrence, indicating that trade routes in higher resolution and local context were connected closer to plague outbreak. One possible explanation for this was that plague entered these local trade routes through the major trade route network, although it remained unclear whether this explanation could be applied in other countries.

To sum up, this study illustrated a plausible pathway for plague transmission in Europe in AD1347–1760. It had important implications in explaining how the plague outbreak pattern was shaped, and how the plague hotspots were generated, by major trade routes. The sign of permanent plague reservoirs in the inland of historical Europe could not be substantiated with strong evidence. Yet, it remains possible, according to the statistical result, that a plague reservoir once existed at the trade ports. The correlation between navigable rivers and sporadic plague outbreak cases might supplement the current explanation of plague distribution, which might provide new insight in examining the geographic patterns of plague. We did not exclude other plausible explanations for plague distribution, as there might be other factors favoring or hindering plague outbreaks in different temporal and spatial domains. Future works should focus on whether our proposed mechanism behaves differently in other spatio-temporal settings. Also, assessing whether a clustering effect in time or space exists might help explain sporadic cases, which is useful in forecasting future plague outbreaks. Most importantly, the case study result of Germany augments the high resolution trade route dataset in explaining more of the relationship between trade route and infectious disease in history. Our findings may contribute to plague prevention and mitigation, especially in the Third World where living conditions and transportation means are similar to those in pre-industrial Europe. Both major transportation routes and navigable waterways are high risk areas to be closely monitored.

## Methods

### Data

Our geo-referenced trade routes data were retrieved from the Old World Trade Routes Project built by Ciolek24. We combined the datasets of Evans and Brooke41 and Spufford42 to reconstruct the major trade route network from late medieval Europe to early modern time. The local trade route in Germany is originated from the study of Davies et al.47. Our geo-referenced plague outbreak data came from the database of Büntgen et al.25. Their work was originated from the literature review done by Biraben48. The geo-referenced database also provided coordinates for latitude and longitude of each plague outbreak case. Elevation data came from measurement through ArcGIS. Vegetation cover data of historical Europe come from the study of Kaplan et al.49. Population density was calculated from dividing the historical demographic figure from McEvedy and Jones50 by current regional area51. It was further normalized according to the data of historical urban area49. We retrieved the per capita Gross Domestic Product (GDP) data for our study area from the database of Bolt and Zanden52 and Maddison53. Consumer Price Index (CPI) and normal laborer’s wages were obtained from the study of Allen54. North Africa indicator included plague outbreaks that happened in North Africa and Turkey. Coastal indicators referred to plague outbreaks that happened at a point less than 5 km to the current coastline. Data on distance of river were acquired by measurement in ArcGIS. The definition of navigable river was based on the study of McGrail55 and Eckoldt56 and therefore we only included rivers wider than 5 m and those rivers that have a connection with other cities. We only measure rivers within a 10 km radius of plague outbreak points. For those cases where rivers were too small or too far away from plague outbreak points, 10,000 m was manually set as the distance. Please refer to SI Text for the details of our datasets.

### Ordinary Least Square (OLS) estimation

We hypothesize the pattern of plague outbreak to be determined by trade routes. To validate the robustness of the above relationship, we include various control variables in our regression models. Our base regression model is:

$$\,{P}_{c}=\propto +\beta (log{D}_{i})+{{\mathscr{X}}}_{i}^{\text{'}}\delta +{C}_{i}^{\text{'}}\varphi +{\varepsilon }_{i},\,$$
(1)

where P c is the total number of plague count at an individual point, $$\propto$$ is the intercept of the equation, $$\beta$$ is the coefficient of the association, $$log{D}_{i}$$ stands for the logged distance to the closest major trade route from each individual plague outbreak point, $${{\mathscr{X}}}_{i}^{\text{'}}$$ is the vector of controlled variables in the model, $${C}_{i}^{\text{'}}$$ is the country fixed-effects estimator that controls the differences among regions, $${\varepsilon }_{i}$$ is the error term. Time fixed-effects estimator is only added to those models with time variants. The relationship between trade route and plague outbreak remains significant even if the time-fixed effects estimator is excluded. The above method is also applied in the remaining parts of our statistical analyses.

### Robustness checks

We perform various robustness checks to validate the significance of our results in different temporal and spatial domains. We built different regression models to explore the impact of trade routes on plague outbreak patterns in different regional settings. This helps to avoid the potential regional discrepancies that are not controlled in our models. Furthermore, factors such as technological improvement are hard to quantify, but they are related to the performance of trade routes over time. Therefore, we slice our data into different time sections to see whether trade routes were still significant in shaping plague outbreak pattern over time. The results of these robustness checks are presented in the Appendix.