Downloadable worldwide database of disease statistics?
I took a quick peek and HealthMap and their JavaScripts are publicly viewable.  As such, I believe cross site scripting would be quite feasible.  In other words, call their JavaScripts from a page you develop on your server to create a feed of the data you want.  

In this way, minimal effort on your part could leverage their data scraping efforts.  If you're adding your own data then you're basically doing a Mashup. 

That said, my concern with doing this is potentially violating their copyright.  I would email them saying if their database is not available then you wish to use cross site scripting to access this data for your project, and unless they let you know otherwise by (specific date) you will assume this is acceptable.

I'm not a lawyer, so use this advice at your own risk.  =)