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Fit as a flea
Mathematical modelling of past infectious disease outbreaks can shed light on both biology and history, write ROX MIDDLETON, LIAM SHAW and JOEL HELLEWELL

FLEAS are flightless parasitic insects that live from drinking the blood of animal hosts. They can jump huge distances using their powerful back legs, allowing them to transfer between hosts. 

Many species of flea are named after a specific host, such as the “cat flea” (Ctenocephalides felis), but are in fact capable of feeding on several different animals. 

As one of the Science and Society authors recently found out from moving into a new house, fleas lurk in carpets and soft furnishings while waiting for a new host. Once bitten, the host will have itchy, red bites.

Historically, being bitten by fleas could have had much worse consequences than just an itchy bite. Several species of flea can transmit Yersinia pestis, the bacterium that causes plague. 

In the case of infection by biting, the bacteria travel to the lymph nodes, producing a swelling known as “buboes.” This type of plague is known as “bubonic plague.” 

The other common form is pneumonic plague, where transmission occurs through the air from one human to another. Both forms are extremely deadly. Left untreated bubonic plague will kill six out of 10 people that are infected.

Historical outbreaks of bubonic plague still present puzzles for modern scientists. For example, how exactly was the plague being transmitted? 

Until recently, all transmission was thought to occur due to rat fleas (Xenopsylla cheopsis) that happily bite both rats and humans. A plague outbreak can occur in rat populations and when a rat dies the fleas living on it seek a new host, including humans that live nearby. 

Just as with Covid-19, mathematical models can be used to study historical outbreaks of plague. The flea-rodent-flea model of plague transmission was the most accepted theory of plague transmission during historical European plagues. 

However, recent work has suggested that the direct transfer of fleas between humans could also have played a significant role. This is based on analysing historical records and looking at the time between recorded infections. 

Each new step in a chain of infection introduces a delay between that organism (be it human, rodent, or flea) becoming infected and becoming infectious themselves. 

Especially within the same household, the subsequent cases of bubonic plague observed in the village of Eyam in Derbyshire were so close together that the evidence fits more closely with fleas moving from one human to another rather than repeated flea introductions from rats. 

Similar work was then reproduced at a larger scale using data on plague deaths in nine European cities, finding that the human-to-human flea model was noticeably better at explaining the data in seven of the cities. 

This would be a good thing in terms of the risk of plague transmission now, since carrying human fleas is far less common now than during the Black Death.

However, bubonic plague still can be and still is transmitted from fleas moving from rodents to humans. Several thousand plague cases are reported each year, with many more likely going unreported. 

Plague persists in rodent populations across the world in low levels. However, it occasionally explodes in large rodent outbreaks that hugely increase the likelihood of plague being transmitted to humans. 

Another ongoing research question is why plague only sporadically explodes in rodent populations. Researchers at the University of Oslo have recently found a potential biological mechanism that would answer this question.

After a flea is infected with Y pestis, the plague bacteria reproduce and form a film that eventually entirely blocks the valve leading from the oesophagus to the midgut. 

As a result, when the infected flea goes to take another blood meal the freshly swallowed blood is vomited back up into the bite wound along with some of the bacteria and causes infection. 

The infected flea also eventually dies of starvation because it cannot swallow a meal. This stage of flea infection, known as being “blocked,” is the most transmissible since the flea reliably vomits considerable amounts of bacteria into the wound.

In addition to being blocked, a flea can also be “partially blocked” where the film does not quite cover the valve into the midgut. 

Some blood can still flow back out into the wound. Transmission can also happen before any blockage has occurred and can happen as soon as when the flea next takes a blood meal as little as three hours later. 

This “early phase” transmission is both far less likely than when a flea is fully or partially blocked and seems to inject far less bacteria into the host.

The researchers in Oslo put together a mathematical model that combines this observation with the fact that rats seem able to develop resistance to Y pestis if they are exposed in small doses. 

Early phase transmission is not reliable enough to cause a widescale outbreak of plague within rodents, but it does cause resistance in a proportion of the rodent population. 

This resistance proportion acts to keep plague in what is called a “steady state” where it doesn’t die out but also doesn’t take off.

Larger outbreaks in the model were due to blocked fleas infecting rodents with much higher doses of Y pestis that overcame their resistances. 

How quickly fleas become blocked after infection, or whether it happens at all, varies depending on the source of the blood. Fleas were less likely to become infected or blocked when feeding on mouse blood compared to rat blood. 

A complex interaction between rodent species, flea species, and previous infection seems to determine if and when larger outbreaks occur.

All disease modelling that doesn’t look to a future that is yet to happen is, in a sense, historical. The methods of the history of disease should include mathematical modelling. 

Yet such modelling, just as with Covid-19, is not purely scientific. It needs to be placed in a historical context to understand the social conditions that lead to the spread of disease: cramped conditions, poor housing or livelihoods that require exposure to dangerous diseases. 

Sometimes reasoning about the past can help us formulate the questions that will help in the present. 

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