The spatial scale, runtime speed, and behavioral detail of epidemic outbreak simulations altogether require the use of large-scale parallel processing. Here, an optimistic parallel discrete event execution of a reaction-diffusion simulation model is presented. Rollback support is achieved with the development of a novel reversible model that combines reverse computation with a small amount of incremental state saving. Parallel speedup and other runtime performance metrics of the system are tested on a small (8,192-core) Blue Gene / P system, while scalability is demonstrated on 65,536 cores of a large Cray XT5 system. Scenarios representing large population sizes (up to several hundreds of millions in the largest case) are exercised.