Tuberculosis Modellers Learn their ABCs

Advances in maths and genomics are taking epidemiology places it’s never been.

Tuberculosis (TB) is one of the top 10 killers globally. In 2016, there were 600,000 new cases that the best available antibiotics could not treat, so it’s crucial to understand how the spread of the disease will change with these new drug-resistant strains.

A supercomputer experiment involving Western Sydney University scientists is providing that key, which could help save lives globally.

In 2009, Andrew Francis, a professor at the University of Western Sydney, joined with a group of mathematicians, physicists and computational biologists to carry out an experiment using a supercomputer hosted at the University of New South Wales.

The researchers used experimental data which linked the genotypes (DNA information) of TB bacteria with their phenotypes (the characteristics of the organism) in laboratory settings. This data indicated that, at least in petri dishes, antibiotic-resistant TB didn’t spread as quickly as non-resistant strains.

That didn’t necessarily mean the same would be true in people, however. To understand the real-world implications of the lab tests, Francis, a mathematician, and his colleagues applied a new modelling approach called Approximate Bayesian Computation (ABC). It allows for the calculation of probabilities based on relevant background information, even when the dependence of those
probabilities on model parameters is intractably difficult to compute.

It’s as though the computer performed an epidemiologist’s fantasy experiment. The computer effectively took 4,000 people with infectious tuberculosis (TB) and monitored the transmission of their disease for 40 years. Then the computer rewound the clock, tweaked the genetics of the bacteria, and ran through 40 years again. It did this tens of thousands of times, keeping watch for the signature of antibiotic resistance and its effect on transmission rates and bacterium survival.

Need to know

  • Supercomputers have modelled TB transmission 
  • They found antibiotic-resistant TB would infect just as many people as the standard 

The researchers calculated hypothetical real-world TB behaviour from the laboratory data using only eight parameters, half of which were fixed to literature estimates. This pared-down scenario predicted that, despite the observations in the laboratory, the relative fitness of resistant TB strains was similar to antibiotic-sensitive strains. This means that antibiotic-resistant tuberculosis bacteria would infect just as many people with TB as the kind that succumbs to treatment.

“In the wild, on average, each individual with a resistant strain is still infecting the same sort of numbers as an individual with a sensitive strain would,” Francis explains.

It’s an important conclusion that would have been impossible to arrive at through laboratory work alone. The model also suggested that virtually all resistant cases arise from transmission, rather than failed treatments, and that antibiotics reduce the prevalence of TB in a population, but raise the proportion of resistant cases.

The findings demonstrate the unique power of combining new Bayesian statistical approaches, new mathematical models and genomic data, an approach that continues to evolve and find new applications. In a second paper, Francis and his colleagues applied ABC to compute the real-world probabilities of TB acquiring resistance to two drugs simultaneously.

How is the broader scientific community taking to the new approach? “It is a very complicated methodology,” Francis says. “They’re not standard modelling approaches.’

But, Francis argues, techniques like ABC are valuable and necessary. “With the advent of new genetic technologies, the complexity of data has just exploded and you can’t apply traditional methods to those data.” In other words, a growing sophistication in laboratory methods needs to be met by increasingly advanced models. And with ABC the work has already begun.

Meet the Academic | Professor Andrew Francis

Professor Andrew Francis is the Director of the Centre for Research in Mathematics at Western Sydney University.He is a former ARC Future Fellow, who works on a wide range of research problems in algebra and mathematical biology.  He joined Western Sydney in the year 2000 as a Lecturer in Mathematics, after a post-doctoral position at the University of Virginia.

While his research is in a wide range of fields, it can be characterized as the application of discrete and combinatorial mathematics, especially reflection groups, to problems.  Apart from algebra itself, these problems have chiefly been in epidemiology, bacterial genome structure, phylogenetics, and statistics. 

Professor Francis has held a number of governance posts, including serving on the Academic Senate 2007-2011.  He chaired the Senate's Mathematics Expert Advisory Group in 2010 that reviewed issues relating to all levels of mathematics at the University and made many recommendations. He has served on the Council of the Australian Mathematical Society (2012-14), on the ARC Research Evaluation Committee for the 2015 and 2018 Excellence in Research for Australia exercises, and on the ARC College of Experts (2018-2020). 


Future-Makers is published for Western Sydney University by Nature Research Custom Media, part of Springer Nature.