Tons - in addition to the split between stochastic (statistical) and deterministic (mathematical) formulation, there's individual vs. population averaged models

Tons - in addition to the split between stochastic (statistical) and deterministic (mathematical) formulation, there's individual vs. population averaged models, various kinds and types of spatial generalizations, an alphabet soup of additional compartments (SEIR and SEIRS being probably the most common), generalizations of the compartment membership time (check out PS-SEIR models), and much more.