Math study link to global disease spread

Research published by La Trobe University mathematicians in the prestigious international scientific journal, Proceedings of The Royal Society, may help to better predict the global spread of infectious disease epidemics – and freak waves such as tsunamis.

Highlighting the importance of advances in maths and their application to everyday problems, the five-member international research team was headed by Dr Peter Van Der Kamp and Professor Reinout Quispel.

Professor Quispel explains that their study looks at stable quantities in systems. 'In Isaac Newton's famous work on the orbit of the earth the stable quantity is energy. This idea is then used to help predict the motion of the Earth around the Sun,' says Professor Quispel.

The La Trobe team has discovered new systems that have many stable quantities. A real-world application of such a system could be the design of better models to predict the likely spread of epidemics, like the current Ebola outbreak in Africa.

Dr Van Der Kamp says other fields in which a sound understanding of this idea is important include the motion of freak waves such as tsunamis, the movement of waterways and the behaviours of particles in physics.

Other members of the research team are Dr Dinh Tran and Dr Theodoros Kouloukas from La Trobe University and Professor Pol Vanhaecke from the University of Poitiers, France.

The title of the research paper is: Integrable and superintegrable systems associated with multi-sums of products.

For those interested in the detail, Professor Quispel explains that the stable quantities in systems are referred to as an 'integral'.

In basic models of epidemics, this integral is the sum of the number of 'susceptible' + 'infected' + 'removed' people in a population.

So the equation looks like this: S + I + R = the integral, or stable part of the system, where

 'Susceptible' represents the number of people not yet infected with the disease, or susceptible to the disease

 'Infected' denotes the numbers who have been infected and are capable of spreading the disease to those in the susceptible category, and

 'Removed' means those who have been infected and then removed from the disease, either due to immunization or death, and can not be infected again or transmit the infection to others.

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