By Carrie Cox

Researchers at The University of Western Australia are using a branch of mathematics known as ‘complex systems’ to help tackle real-world mental health challenges including the likelihood of young people to self-harm and the treatment of Indigenous patients in hospital settings.

Complex systems mathematician Professor Michael Small, who is also Director of the UWA Data Institute, is a Chief Investigator on a number of research projects that operate at the coalface of mental health treatment in WA.

Complex systems mathematics involves networks that comprise multiple components that interact with each other, often in a non-linear way.

Image: Professor Michael Small.

Professor Small’s research team has worked extensively with Perth Clinic to turn inpatient surveys into mathematical models of self-harm prediction, ultimately informing the structure of nursing schedules to ensure people at higher risk are under closer watch.

The Perth Clinic project is now being translated into the WA school system, with an initial 12-month survey phase now being rolled out to metropolitan schools.

“It’s a proof- of- concept project initially that will focus on predictors of self-harm and covariates of psychological distress among school students who present to psychiatric nurses and chaplains,” Professor Small explained.

“One of the overarching goals is not to make predictions about cohorts but rather about individuals.

“Knowing what group is likely to self-harm is helpful from a resources point of view but not so helpful in terms of how you effectively treat an individual within that group.”

An individualised approach is also central to another of Professor Small’s research projects that is looking at the journey of Indigenous patients through the mental health system in Albany.

“It’s an expansion of a study we did several years ago in Perth that looks at how the different actors in a hospital play roles that interact with patients and their data and identifying which roles may be instrumental to the efficient flow of vital health information and to a patient’s wellbeing,” he said.

“This Albany study is focused more broadly on Indigenous wellbeing and to the delivery of culturally appropriate care.

“We’re looking at individual stories and trying to build a mathematical model that interprets data in a meaningful way – and we’re already getting some interesting results in terms of which roles are more important and which parts of the system are particularly stressed.”

Professor Small said while traditional maths had limited application for networks as complicated as public health, complex systems mathematics made for a good fit.

“Complex systems maths is very visual and intuitive compared to traditional maths and can present a different way of looking at a problem,” he said.

“On its own maths is not the answer, but it can form part of a broader view of things.

“For example, a huge part of the Indigenous health project is simply listening to people and understanding the challenges they’re experiencing in a health system that was set up for a different audience.

“Maths is not driving the project or delivering the results, but the patterns it finds and the models it creates can help to inform the questions being asked about how we can improve the system.

“For me, research has never been about just producing papers – I want to know that what I’m doing is making an impact on people’s lives.”