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# Keeping invaders at bay with mathematics

They’re only a few millimetres long, but these aggressive invaders pack a painful sting that burns and itches for up to an hour. With a coppery-orange head and a dark-brown abdomen, red imported fire ants are on the move across Australia.

Native to South America, the fire ants are now an invasive pest in Queensland and parts of New South Wales. Opportunistic feeders, they prey on small animals and plants. And if they can’t be stopped, they could wreak havoc on our farmland and some native species.

The people in charge of stopping their spread – Biosecurity Queensland – have tried to eradicate the ants, but weren’t sure if their programs were working. They needed a mathematical model that could put their programs to the test. For help, they turned to MAXIMA – a part of the Monash Technology Research Platforms (MTRP).

Otherwise known as the Monash Academy for Cross & Interdisciplinary Mathematical Applications, the experts at MAXIMA had the essential knowhow in mathematical modelling to calculate a new approach to dealing with fire ant infestation.

Fire ants spread very quickly. Using data from a Brisbane fire ant invasion back in 1996, MAXIMA’s mathematicians studied the spread of the ants, month by month. Using a technique called agent-based Bayesian modelling, the maths whizzes revealed that the crucial aspect of containing the ants was to determine their invasion boundaries – the limits to where their nests can spread.

Invasion boundaries move around. So, a successful eradication program must be able to predict the rate and direction of this movement. If invasion boundaries can be accurately estimated at the time of an initial outbreak, authorities can reallocate resources and funding to the regions that need it most.

For the most part, previous attempts to eradicate these invasive pests have failed. Now, with the mathematical power of MAXIMA behind them, researchers can estimate invasion boundaries and keep one step ahead of the ants. As an added bonus, the models of one invasion can be adapted and applied to other biological problems – such as the spread of bird flu and other diseases.

Having the right tools, such as Bayesian modelling, can improve the field of invasion biology and eradication strategies. In turn, this can reduce the huge environmental, social and economic costs of invasive species. But without the mathematical genius of those at MAXIMA, the complicated process of modelling would be impossible.

Through the open-access research model of MTRP, MAXIMA provides easy, coordinated access to mathematical minds who can help solve important environmental, economic and societal problems. Apart from calculating fire ant trajectories, MAXIMA’s mathematicians also provide solutions for problems that range from understanding stem cells and embryo formation to improving road traffic flow.