# Mathematics Across Disciplines

3 pm to 3.30 pm - Afternoon tea

Time: 3.30 pm

Speaker: Kathryn Glass (NCEPH)

Title: Mathematical models of infectious diseases: understanding transmission and interference between pathogens.

Abstract:

Mathematical models play a key role in control of infectious diseases.  They can be used to support the epidemiological response to disease outbreaks, such as that of Ebola in 2014/2015, or to predict the likely benefit of a new vaccine for respiratory illness.  An emerging challenge in disease modelling is to take account of the potential interaction between pathogens.   Negative interactions can occur very simply through human behaviour: sick people are more likely to stay away from others and so are less likely to be infected with a different pathogen.  There are also more complex biological and immunological interactions, where infection with one pathogen can make individuals either immune to, or more susceptible to, other pathogens.  I’ll give examples of data showing two different interaction effects and discuss how we might capture this behaviour using mathematical models.

Time: 4.10 pm

Speaker: Jason Sharples (UNSW Canberra)

Title: Mathematical modelling of the dynamic evolution of wildfires

Abstract:
The behaviour and spread of a wildfire are driven by a range of processes including convection, radiation and the transport of burning material. The combination of these processes and their interactions with environmental conditions govern the evolution of a fire’s perimeter, which can include dynamic variation in the shape and the rate of spread of the fire. It is difficult to fully parametrise the complex interactions between these processes in order to predict a fire’s behaviour. In this talk we will consider some of the ways that fire propagation is modelled. In particular, we will discuss the use of coupled fire-atmosphere models and present some recent results pertaining to specific scenarios where fires interact dynamically with the surrounding atmosphere. We will also consider using geometric aspects of the fire's perimeter, defined as the interface between burnt and unburnt regions, as simple alternatives to model dynamic fire spread. Specifically, we discuss the use of local fire line curvature and introduce the concept of pyrogenic potential flow. Incorporation of such geometric dependence in an empirical fire propagation model provides closer agreement with the observed evolution of experimental fires than traditional approaches to modelling fire spread. Fire spread models incorporating geometric dynamics therefore offer a computationally efficient alternative to fully coupled fire-atmosphere models, and may lead to improved capability for operational fire spread prediction.