Art Courtesy of Hannah Dirsa.
Measles was first introduced to Fiji in 1875. It died out only six months after its debut.
The introduction of measles to the Pacific Islands is often painted as a straightforward superspreader event, but the reality is that measles didn’t become the outbreak we know it as until it was reintroduced in 1903. “There’s a story of global disease history in the popular imagination that says diseases spread like wildfire across the globe once European colonists started sailing on their ships,” said Elizabeth Blackmore, a graduate student in the Department of Ecology and Evolutionary Biology at Yale. However, this story is an inaccurate one, and her work gives reason as to why.
A recent paper by Blackmore and James Lloyd-Smith, a professor of ecology and evolutionary biology at the University of California, Los Angeles, deepens our understanding of how diseases spread across oceans and the likelihood they will take hold in a population. They seek to poke holes in popular, yet false, narratives about disease.
Moving beyond the simplistic notion that every single case has the potential to spark a superspreader event, the paper presents a model that offers a detailed quantitative framework for analyzing infectious disease spread aboard ships.
A New Approach to Understanding Outbreaks
The model, known as a stochastic Susceptible-Exposed-Infectious-Recovered (SEIR) model, aims to quantify the probability of an outbreak lasting a particular length of time within a certain population. It was inspired by studies on epidemics in California, where the researchers noticed that measles had been introduced relatively late, in 1806. This unexpected finding spurred them to develop this mathematical model to explore the reasons behind it.
“How did it take that long? How did measles even get to California?” Blackmore said. “How easily could measles survive on a ship?”
Blackmore described the model as taking a classic approach. “Because this is the first general study of how long outbreaks last onboard ships, we intentionally decided to take one of the simplest approaches we could think of,” she explained.
Using established outlooks and parameters from traditional infectious disease studies, Blackmore and Lloyd-Smith built their model of disease spread during transatlantic voyages. This approach enabled them to quantitatively analyze events that had previously only been addressed qualitatively. Their efforts marked the first time these issues had been evaluated through a numerical lens.
The model begins by examining susceptibility—determining whether a given individual within a population is capable of contracting the disease. To simplify the initial analysis, the model first assumes that the entire population is susceptible, which allows them to create a baseline for their model. The researchers later explored varying percentages of susceptible individuals to see how different levels of immunity could influence disease transmission patterns.
Next, the researchers incorporated two critical timeframes: the incubation period, which refers to the time from infection to symptom onset, and the infectious period, which is the duration a person can transmit the sickness to others. In addition, they factored population size into their model.
Another important element is the epidemiological parameter, or R0, which represents the average number of infections caused by a single person in a fully susceptible population. By manipulating R0, the researchers could observe the dynamics of disease spread. A very low R0 indicates that the virus does not transmit beyond the initial case—thus, the outbreak lasts only as long as the first person is incubating the virus. Conversely, when R0 is very high, the virus continues to spread among individuals and is only stopped when herd immunity is achieved—that is, until enough people are no longer susceptible to the disease, which ultimately slows down and can halt transmission. This situation results in outbreaks that last longer, as the virus has a larger pool of potential hosts to reach before it can no longer spread effectively.
Interestingly, the longest outbreaks occur when R0 is at an intermediate “critical” value. Around this range, the outbreak can last up to thirty times longer than the average length of an infection in a single individual, though durations can vary greatly. While R0 serves as the foundation for their initial, simpler model, Blackmore and Lloyd-Smith later refined this value into the pathogen effective reproduction number (Re), a more nuanced representation of transmission intensity.
Measles in California
Focusing on steamship journeys between 1850 and 1852 to and from a port in San Francisco, Blackmore and Lloyd-Smith used the model to analyze the transmission of measles, influenza, and smallpox, demonstrating how each disease’s distinct characteristics influenced their spread.
The model demonstrated that disease transmission, even via ship travel, can be slow and depends greatly on specific disease traits. For instance, influenza has a very low R0 and very short incubation and infectious periods; based on the model’s calculations, only the most rapid journeys with a high volume of passengers could have facilitated the introduction of this disease to California. In contrast, measles, which has longer incubation and infectious periods, poses a moderate risk. Smallpox poses a great danger even on extended journeys due to its prolonged incubation period. However, its low Re means that transmission within a population, and therefore widespread introduction throughout a city, is still unlikely.
In addition, the model sheds light on important historical events. “Even Christopher Columbus’s famous 1492 journey had a decent chance of carrying a virus like measles or smallpox across the Atlantic—if an infected sailor had been among the crew at departure,” Lloyd-Smith said.
Charting a Path for Future Disease Prevention
Blackmore emphasizes the importance of viewing infectious diseases through a more human-centered lens. “You’ll see everywhere people saying that ships carried disease. And it makes it sound like the disease is sitting in a box, along with a whole bunch of other cargo,” Blackmore said. “I think it’s important to write histories of infectious disease where we take the experience of infection seriously.”
The researchers continue to work on validating the model by comparing its predictions to even more historical sources, such as ship medical logbooks and quarantine station records, to test their confidence in its predictions. Future work could also improve the model by introducing more complexity to its components. For example, instead of assuming everyone in the population is equally susceptible to a disease, a new model could take variations in individuals’ susceptibility into account. Additionally, parameters could be added to consider that some diseases can be spread through non-human routes, such as surface contact or vectors like rats. Finally, the roles of infected individuals on the ship can also influence risk levels.
Blackmore hopes to use her research to educate the public about historical disease transmission. However, she also emphasizes her work’s relevance to contemporary issues, such as COVID-19. “We can’t expect people to believe that social distancing works if we are telling stories about how ships spread pathogens across the world like magic,” Blackmore said.
Modeling infectious disease spread has important implications for both the past and present. However, it could also play a key role in the future. In particular, space travel could be a perfect candidate for Blackmore and Lloyd-Smith’s model. “There are strong similarities [to ships], with small populations of humans aboard a vessel for extended periods, journeying to new areas that may not have encountered some of our human pathogens before,” Lloyd-Smith said.
Blackmore noted that pathogens with longer lifespans would be especially relevant in space environments, citing tuberculosis as a prime example. With potential advancements in space travel technology, however, it’s possible that even measles could become a concern.
“If humans establish a colony on Mars, we would like to avoid introducing pathogens from Earth if we can avoid it,” Lloyd-Smith said.