Disease trackers analyze the aftermath

Canadian epidemiologists are devising math formulas
to predict the spread of disease

By Graham Furness

Does complex math make your head hurt? Rest assured that it can come in pretty handy ... sometimes. Math can help predict the spread of natural disasters like forest fires. But wouldn't it be great if we could also predict the spread of epidemics? Not to worry. Math whizzes are formulating a model as we speak.

Sometimes when gauging how outbreaks are going to spread, however, seemingly similar situations can produce radically different and apparently unpredictable results. A case in point is SARS. One of the first two SARS patients in Canada flew from Hong Kong to Toronto, infecting hundreds while the other flew to Vancouver, but in this case the disease failed to take root.

In retrospect, even the mini-epidemic in Toronto and the far more serious situation in China fell way short of the apocalyptic predictions made when SARS first reared its head. The different Chinese and Canadian experiences with SARS highlight the strengths and weaknesses of the nascent science of mathematical modelling of epidemics.

Chinese doctors made calculations based on the number of new cases infected by the first few SARS patients. Extrapolating from that, they concluded that the epidemic was essentially unstoppable. In fact, their model predicted that the entire human race would soon be infected.

It didn't happen, and the reason why not became apparent when Canada set out to analyze its own SARS outbreak with more advanced mathematical modelling. Dr Babak Pourbohloul of the University of British Columbia collaborating with Dr Lauren Ancel Meyers from the University of Texas at Austin attempted to apply network theory to the problem.

Dr Meyers explains the basic principle: "Each person within a community is represented as a point in the network. The edges that connect a person to other people represent interactions that take place inside or outside of the home, including interactions that take place at school or work, while shopping or dining, while at a hospital, etc. The network thereby captures the diversity of human contacts that underlie the spread of disease."

The original estimates of transmission rates for the SARS virus approximated those of a new subtype of influenza. Applying a standard equation to these estimates predicts that in the first 120 days of transmission in China, there should've been between 30,000 and 10 million new cases. In fact only 782 cases were reported during the initial three months.

The Chinese mistake, in essence, was to extrapolate rates of infection from an initial hospital outbreak into the wider population. All mathematical modelling of infectious disease starts with a fundamental quantity called the basic reproductive number � the number of new cases resulting from a single initial case. But in a hospital environment, it was practically inevitable that the first few cases would each infect more than one other person. Extrapolating from that, a simple mathematical model will always predict a large-scale epidemic. Somehow the Chinese overlooked this.

"The contact patterns of the first few cases can make all the difference as to whether you get a big outbreak or epidemic or none at all," says Dr Meyers. It's essential to model the different social interactions in a population to really predict disease spread.

Drs Meyers and Pourbohloul are currently working with a large team of Canadian epidemiologists on network models of four Canadian hospitals and two communities � one rural and the other urban. These models, they hope, will help predict and control the spread of all kinds of diseases.

Viruses that jump directly between people are the simplest diseases to model. But mathematical modellers are also aiming at diseases with other, environmental factors. Efforts are underway to model malaria and dengue fever. Mosquitoes, however, don't stand around waiting to be counted, and the predictions soon run into a ubiquitous mathematical problem, which is that small errors in the initial data mushroom as the projections look further ahead.

One of the world's most acclaimed environmental modellers of disease in Florida, Dana Focks, PhD, set up a basic early-warning system that accurately predicted the spread of dengue in Indonesia up to three months ahead, but by his own admission his efforts at modelling the same disease in Thailand were less successful. When the US Centers for Disease Control and Prevention asked him to create a model to describe the spread of West Nile virus, he refused, saying there were too many hosts, and not enough known about them.