DescriptionThis project is aimed at deriving and obtaining information on models for an epidemic. Recent cases of the spread of epidemics are many, e.g. SARS, Foot and Mouth disease, Mad Cow disease, and many more. In the project you will be able to look at various models for the spread of epidemics. For example you could start with an SIR model, then generalize to SIRS models, SEIS models (where the E class denotes infected but not yet infectious), SIVS models, and others. Spatial propagation could also be taken into account via diffusion terms and analysis of travelling waves.The mathematical part will involve analysis, not unlike that covered in the 3H Math Biology course, so, stability/instability analyses, travelling waves where necessary. However, in a project you could use numerical solution of ODEs to actually examine the solution behaviour for various parameter ranges. The project would then take on various avenues. For example, you could analyse particular data for a specified disease and then see how good your model is. Another option would be to use various numerical schemes and see which gives the most accurate results (in this event the chapter on ODEs in Burden and Faires would come in very helpful). There are many ways this project could take shape, and the above is just a possibility. PrerequisitesMathematical Biology III, Numerical Analysis II and a willingness to do computer simulations. |
email: James Blowey Brian Straughan