In simulation-based studies and analyses of epidemics, a major challenge lies in resolving the conflict between fidelity of models and the speed of their simulation. Another related challenge arises in dealing with the large number of what-if scenarios that need to be explored. Here, we describe new computational methods that together provide an approach to dealing with both challenges. A mesoscopic modeling approach is described that attempts to strike a middle ground between macroscopic models based on coupled differential equations and microscopic models built on fine-grained behaviors such as at the individual entity level. The mesoscopic approach offers the possibility of incorporating complex compositions of multiple layers of dynamics even while retaining the potential for aggregate behaviors at varying levels. It also provides an excellent match to the accelerator-based architectures of modern computing platforms in which graphical processing units (GPUs) can be exploited for fast simulation via the parallel execution mode of single instruction multiple data (SIMD). The challenge of simulating a large number of scenarios is addressed via a method of sharing model state and computation across a tree of what-if scenarios that are localized, incremental changes to a large base simulation. A combination of the mesoscopic modeling approach and the incremental what-if scenario tree evaluation has been implemented in software on modern GPUs. Synthetic simulation scenarios are explored and presented here to demonstrate the basic feasibility and computational characteristics of our approach. Results from the experiments on large population data illustrate the overall modeling methodology and computational run time performance on large numbers of synthetically generated what-if scenarios.