I applaud your ambition; this is quite a difficult project to do at sixth form level, but if you are comfortable with the ordinary differential equations that you’ve studied at this level, you should be able to do something interesting.
The very basic models for tumour growth are based on ideas nicked from population biology: the tumour cells are considered to be one “species” competing against the non-tumour cells. So, exponential models are derived from little or no competition, and the logistic model is a classic example of a model of species competition. Similarly, the Gompertz model, and the Bertalanffy model. I would think that at your level, a project comparing just these basic models would be quite enough.
Are you able to get hold of a copy of Britton’s “Essential Mathematical Biology”? It’s got a good chapter introducing these models. Also, perhaps, take a quick look at this paper:
https://bmccancer.biomedcentral.com/articles/10.1186/s12885-019-5911-yIt provides a not-too intimidating introduction to these sort of models, has some tumour growth data and looks at model fit. It’s probably also right at the limit of what’s accessible to you.
Don’t! This is way too hard. Modern chemotherapies can be as complex as targeting individual cell-signalling pathways in tumour cell – you’re looking at the prospect of stochastic partial differential equations here. Scary!
Best place is probably to extract it from the supplementary materials of open-access journal papers online. Google search “tumor growth data” turns up quite a lot.
A lot of the early models in this field were phenomenological models – taking observed data and trying to fit simple differential equations to that data. But pretty soon, theory had to get involved, as the early models were more than a bit approximate. So the logistic model already involves the idea of tumour cells and non-tumour cells as competing forces. Almost all models these days are based on theory: adding on what we know of the processes of cellular biology, immunology, tumour vascularization etc. etc etc. It all gets very complex very quickly!
A key thing, I think, is for you to not take on too much – and as it’s not an assessed project, make sure you enjoy it! So start with the basics, and try and do that well.