2015, Swan, Amanda, Murtha, Albert

The study of mathematical biology attempts to use mathematical models to draw useful conclusions about biological systems. Here, we consider the modelling of brain tumour spread with the ultimate goal of improving treatment outcomes.

2015, Solomon, Tom

Very simple mathematical equations can give rise to surprisingly complicated, chaotic dynamics, with behavior that is sensitive to small deviations in the initial conditions. We illustrate this with a single recurrence equation that can be easily simulated, and with mixing in simple fluid flows.

2015, Eftimie, Raluca

Communication forms the basis of biological interactions. While the use of a single communication mechanism (for example visual communication) by a species is quite well understood, in nature the majority of species communicate via multiple mechanisms. Here, I review some mathematical results on the unexpected behaviors that can be observed in biological aggregations where individuals interact with each other via multiple communication mechanisms.

2014, Benner, Peter, Mena, Hermann, Schneider, René

The Colombian government sprays coca fields with herbicides in an effort to reduce drug production. Spray drifts at the Ecuador-Colombia border became an international issue. We developed a mathematical model for the herbicide aerial spray drift, enabling simulations of the phenomenon.

2015, Marron, J. S.

Statistical visualization uses graphical methods to gain insights from data. Here we show how a technique called principal component analysis is used to analyze mortality in Spain over about the last hundred years. This data decomposition both reflects expected historical events and reveals some perhaps less expected trends in mortality over the years.

2015, Funk, Sebastian

Sleeping sickness is a neglected tropical disease that affects rural populations in Africa. Deadly when untreated, it is being targeted for elimination through case finding and treatment. Yet, fundamental questions about its transmission cycle remain unanswered. One of them is whether transmission is limited to humans, or whether other species play a role in maintaining circulation of the disease. In this snapshot, we introduce a mathematical model for the spread of Trypanosoma brucei, the parasite responsible for causing sleeping sickness, and present some results based on data collected in Cameroon. Understanding how important animals are in harbouring Trypanosoma brucei that can infect humans is important for assessing whether the disease could be reintroduced in human populations even after all infected people have been successfully treated.

2015, Schweizer, Ben

Formulations of natural phenomena are derived, sometimes, from experimentation and observation. Mathematical methods can be applied to expand on these formulations, and develop them into better models. In the year 1856, the French hydraulic engineer Henry Darcy performed experiments, measuring water flow through a column of sand. He discovered and described a fundamental law: the linear relation between pressure difference and flow rate – known today as Darcy’s law. We describe the law and the evolution of its modern formulation. We furthermore sketch some current mathematical research related to Darcy’s law.