Fighting pandemics with mathematics

Researchers from the University of Warwick, the University of Adelaide and the Health Protection Agency have developed a new tool to quantify the spread and infectiousness of viruses during pandemics. It is hoped that the study, which has been published in the journal BMC Medicine, will enable medical professionals to react appropriately to the outbreaks of the future.

H1N1, or swine flu as it was coined in the press, hit the United Kingdom in 2009. It proved very difficult for medical professionals to garner an accurate picture of the virus’s prevalence because many of those affected only exhibited mild symptoms. As such people were unlikely to visit a doctor, it was feared that the overall extent of the outbreak was underestimated. Subsequent blood studies confirmed these suspicions as samples from the wider population suggested that approximately 90 per cent of cases had been missed.

In order to minimise the chances of such discrepancies, the mathematicians set about creating a mathematical model to provide a more accurate indication of a pandemic’s spread. I spoke to Dr Thomas House, one of the study’s co-authors from the Warwick’s Mathematics Institute, to find out how this tool might be used to tackle future pandemics.

"Essentially, we wanted to use advanced mathematics to glean the maximum amount of information from the data that were available," Dr House began. "In particular, we were interested in the way that cases tend to cluster within individual households. Basically, if a virus such as H1N1 reaches one person in a household, there are two common outcomes. Either nobody else becomes infected or many members of the household become infected. If one person passes the virus onto a second person in a household, the risk of a third person becoming infected is doubled. As a result, during pandemics you tend to find many households with very little disease and many with a lot of it. You don’t tend to see many in the middle. This is the opposite of what you would expect to find in normal circumstances. Histograms pertaining to pandemics take the shape of a lower-case u, rather than that of a lower-case n.

"Our model uses this theory to provide an indication of how many cases might have been missed. The vast majority of cases during the 2009 H1N1 outbreak were missed because the symptoms were often so very mild. This is absolutely no criticism of the public health professionals who did a very good job in the circumstances. It is simply a very difficult problem to overcome. How do you account for people who have contracted a virus but do not visit a doctor? We are confident that you can use these u-shaped histograms to predict the number of infections that have been missed."

Whilst 90 per cent seems like a staggering proportion of cases to slip beneath the radar, if the symptoms are so mild, why do such cases matter? As Dr House explained, these cases matter because they enable medical professionals to prepare for the ‘second wave’ of a pandemic.

"Pandemics come in two waves," he said. "When data from the first wave are collected, nobody really knows how severe the second wave is going to be. For instance, the first waves of some particularly deadly pandemics have been quite small. The 1918 Spanish flu pandemic involved a small wave followed by a really severe wave that killed an awful lot of people. There is always uncertainty over how bad the second wave is going to be. In terms of the recent H1N1 outbreak, a more accurate picture of the first wave would have revealed that the second wave wasn’t likely to be as bad.

"If a lot of people contract a virus during the first wave of a pandemic, but exhibit only mild symptoms, they are not going to be infected the second time around. They will have developed immunity to the virus. However, if you don’t account for the individuals who have already contracted the virus, you might overestimate the number of people at risk from the second wave. Our model can help medical authorities to more effectively predict the severity of a second wave. It can help to avoid both under- and overreactions to pandemics."

Dr House is confident that his mathematical model will allow the medical community to make appropriate provisions for the second waves of future pandemics. Even so, he was keen to stress that it is best used in conjunction with other tools.

"Our model proved consistent with other data that were collected," he explained. "All models are based on assumptions. Every model, therefore, is fallible in the sense that the assumptions of mathematicians are not always perfect. However, the u-shaped histogram serves as a very good indicator when it comes to infectious disease. We tested our tool against simulated data and found that when we inputted known parameters, we obtained accurate feedback. Of course, no model is perfect but it is another tool to be used alongside the needle and the stethoscope. It is about using maths in an appropriate way."

I ended our conversation by asking Dr House how quickly his model could be tailored to reveal the likely extent of other diseases, and about the cost effectiveness of this approach.

"Once you’ve done the groundwork, you don’t have to buy needles and vaccines in order to use the model," he replied. "It’s about being smart with the available data. It wouldn’t take too long to adapt this tool. The only resources necessary are the mathematicians’ salaries and perhaps some decent computers on which to code the model. We are hoping to secure funding to develop a desktop application that can be used by anybody, regardless of their level of expertise. The cost of developing such a tool would be comparatively low; it would certainly be a lot cheaper than administering treatments to large numbers of people unnecessarily."