Biomathematics

As the study of biological systems becomes more quantitative, the part that mathematical analysis plays increases. This extends from the macroscopic, such as modelling the spread of a disease through a community, to the microscopic, such as determining the three-dimensional structure of proteins from knowledge of their sequence of amino acids.

Research Interests

  • Nonlinear dynamics of communication between cardiac pacemaker cells, as well as their response to external stimulation
  • Unified mathematical model of the electrophysiology of charophytes (brackish water plants)
  • Dynamics of the movement of glucose transporters in adipocyte (fat) cells and the role of insulin in their expression
  • Multifractal scaling of neuron morphologies to identify age-related characteristics
  • Fractional reaction-diffusion equations as models for pattern formation in systems in which the diffusion is anomalous
  • Modelling transport processes in inhomogeneous biological media ranging from molecular, cellular and network to whole organisms
  • Analysis of neuronal signaling dynamics in inhomogeneous neural cables
  • Methods of nonlinear dynamics to find evidence for low dimensional deterministic chaos in arterial blood pressure data, the first stage in attempting to identify a diagnostic for predisposition to chronic hypertension
  • Immune system dynamics
  • HIV, hepatitis B and C
  • Epidemiology
  • Cancer chemotherapy
  • Dynamics of drug resistance

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