While the population counts are integers, their expected values are real.
Hence, for the deterministic process, we have moved into the realm of "continuous Petri nets."
Whereas for stochastic Petri nets, we can visualize the species as _places_ that hold discrete tokens, now they are places that hold continuous magnitudes.
Picture them as buckets holding a certain amount of "numerical fluid." The processes are then continuous pumps, draining their input buckets, and filling their output buckets.
An analogous law of mass action still holds: the pumping rate of a process is equal to its transition coefficient times the product of the values present at the input buckets.