Predictions in medicine are currently moving in the direction of using of machine learning methods and data mining. This is a very dynamically evolving and complicated area on its own.

Jiri :-)

Matlab, python and R, i have used R for epidemic problems, I recommend mostly R it has a lot of libraries, SIR model are easy job. For example http://www.modelinginfectiousdiseases.org/ this book has the mathematics and codes in python and matlab. I am junior and working in epidemic models for infectios diseases. Hae a nice day :D

When one thinks about software, it is worth to mention Scipy (many algorithms and methods are covered there including machine learning methods) in Python and Weka for machine learning.