The design of reliable numerical schemes for real-life applications is investigated for topical medical question as cancer growth and bone healing.
Two of the most recent Research Chairs awarded by the National Research Foundation are exploring the use of mathematical models in the field of biosciences.
Professor Cang Hui’s Research Chair in Mathematical and Theoretical Physical Biosciences at Stellenbosch University is held jointly with the African Institute for Mathematical Sciences.
Hui says: “Our research tends towards the theoretical side and is concerned with proposing models and theories to explain emerging patterns in whole-organism biology, namely ecology. By running simulations based on a known or assumed biology we are able to identify system thresholds and expected responses that could then be applied for better management intervention of the biological system.”
These types of models could be applied to immunology, for instance, to greatly improve our understanding of the pathogenesis of viruses and our ability to design drugs that could lead to a guided evolution towards low virulence. The same principles can be applied to biodiversity conservation, where modelling would enable scientists to prioritise habitats for preserving endangered species or plan for the eradication of invasive species. This knowledge is especially relevant given the rapidly changing socioeconomic landscape and climate regime.
He says that this line of work ties in with the drive in the biosciences to develop new mathematical and statistical approaches that are suitable for analysing and forecasting complex living systems in a changing world.
Professor Jean Lubuma at the University of Pretoria is also concerned with developing mathematical models that provide insights into biological causes and effects, including the biomedical field.
His Chair in Mathematical Models and Methods in Bioengineering and Biosciences (M3B2) is quite new, although a number of postgraduate students have already been enrolled and are expected to start graduating from early next year. He explains that the main thrust of his work is to model biological processes and phenomena by using differential equations, which are then analysed quantitatively, qualitatively and computationally.
His team is internationally well-known for the design of reliable numerical schemes for real-life applications, an approach that is being investigated for topical medical and ecological questions such as cancer growth and therapy, bone fracture and healing as well as the production and transmission of queen honeybee pheromone.
Furthermore, mathematical analysis could typically be used to model the dynamic transmission of a disease to predict when it will lead to an outbreak, how it is likely to develop and when it is expected to abate.
These types of insights are critical to the medical community in planning public health interventions in the case of the onset of viral and bacterial diseases such as flu, malaria, tuberculosis and HIV/Aids.