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Member Research & Reports

Mathematical Model Developed at Yale Provides New Insights into Deadly Bubonic Plague

The bubonic plague, transmitted by fleas from rats to humans, has caused major disruptions throughout history, from the Byzantine Empire to the Victorian era. Plague—from natural sources and as an agent of bioterrorism—still poses a threat today, leading scientists to look to the past to understand how interactions of fleas, rats and humans can wreak havoc by spreading the disease.


A new Yale School of Public Health study published in the Proceedings of the National Academy of Sciences uses a mathematical model to understand the joint effects of climate on plague-carrying fleas and the evolution of plague resistance in rats. Based on a set of historical experiments and observations from the plague epidemics of colonial India, the analysis sheds light on how rapid evolution in response to disease impacted one of the plague’s most severe outbreaks.

Dr. Jeffrey Townsend, associate professor in the Department of Biostatistics at the School of Public Health, and Mr. Joseph Lewnard, a PhD candidate in the Department of Epidemiology of Microbial Diseases, created the model. They analyzed archival data from India from 1896 to 1911, a period that is known as the third plague pandemic. It originated in China and via maritime trade networks was spread to ports on every continent. The pandemic killed more than 12 million people in India alone.

“The third plague pandemic was deadly and spread quickly around the globe,” Dr. Townsend said. “One could even say that this time was the dawn of the globalization of pandemic disease. The horror of what seemed to be an unstoppable epidemic galvanized extensive record-keeping. But there have remained longstanding, puzzling observations about how plague seasons shifted over time, and why those shifts coincided with the waning of the pandemic.”

Combining datasets prepared by the Victorian-era Indian Plague Commission on plague mortality, rat infection and resistance and the survival of fleas at different temperatures, the Yale researchers developed a model that combined known environmental factors with evolutionary selection of rats, the natural host of the disease in cities. In what may be the earliest experimental evidence of evolutionary responses to an infectious disease, historical investigations in India beginning in 1906 showed a heritable form of plague resistance among rats, which quickly became common in cities severely affected by plague.

By incorporating this evolutionary selection, the model reproduced observed changes in seasonal epidemic patterns in several Indian cities, while capturing experimentally observed associations between climate and flea population dynamics in India. As a result, the researchers show that the declining susceptibility of rats in Indian cities buffered against seasonally triggered increases in plague transmission.

“To say the investigations by the Indian Plague Commission were ahead of their time is an understatement: their studies answered every ecological question that we struggle with today when modeling diseases at the human-animal interface,” said Mr. Lewnard. “It is humbling to substantiate a century-old hypothesis that originated in a time when scientific understandings of evolution and the germ theory of disease were in their infancy.”

The team’s combination of archival data with novel statistical methods demonstrates how historical analyses can yield powerful insights into the transmission dynamics of emerging disease agents, with which modern researchers often have limited familiarity.