Teaching

• 2006-2007, Advanced Partial Differential Equations.
• 2007-2008, Advanced Partial Differential Equations.
• 2008-2009, Mathematical and Data Modelling
• 2009-2010, Continuum Mathematics

Students

• 2007-2008, Wanjiao Li, MEng project on "Modelling of St Mary Redcliffe Church Chaotic Pendulum".
• 2008-2009, Oliver Purcell, BCCS Complexity Student, "Modelling the human intracellular platelet network".
• 2008-2009, Ed Herbert, MEng student project on "Can we predict blood clotting?".

Potential MSc and PhD projects

• Modelling the interactions between plant viruses
  
  Joint project with Dr K Blyuss.

Despite "common sense" expectation that different viruses would inhibit each other when they infect the same plant, experiments show that in fact quite the opposite happens. In many cases, viral infections promote each other instead, and this has a devastating effect for plants. This project will look into simple mathematical models for the dynamics of interaction between viruses and the plant they infect. It is anticipated that a range of analytical and numerical techniques from nonlinear dynamics and chaos will be employed to investigate this intriguing behaviour.

• Mathematical modelling of Hepatitis B Virus

The aim of the project will be formulation and investigation of mathematical model for Hepatitis B virus infection. A particular emphasis will be given to the question of time delay in virus production, which, though omitted in many models, plays an important role in disease dynamics. Dynamical systems tools will be used to study the model, including DDE-BIFTOOL for bifurcation analysis. Time permitting, the interaction between Hepatitis B and HIV will be analysed.

• Time-delayed synchronization in coupled spatially-extended systems
  
  Joint project with Dr K Blyuss.

The project will look into the ways spatially extended systems can be coupled and synchronized using time delay. This is an interesting problem which arises in numerous applications including lasers, chemical reactions and some engineering experiments. The effects of time delay and its interactions with spatial extent will be studied through the analytical and numerical simulations.

• Can we predict Blood Clotting?
  
  Joint project with Dr K Tsaneva-Atanasova and Prof A Poole.

When blood vessels are cut or damaged, the loss of blood from the system must be stopped before shock and possible death occur. This is accomplished by solidification of the blood, a process called coagulation or clotting. Platelets are anuclear cells which play a central role in facilitating blood clotting after a vascular damage. Dysfunction or low levels of platelets pre-disposes to bleeding, while high levels, although usually asymptomatic, may increase the risk of thrombosis. It is envisaged that this project will concentrate on mathematical modelling of platelet activity using ordinary differential equations. Dynamical systems approach including analytical methods and numerical simulations/continuation will be used to investigate influence of different environmental factors on the platelet activities.