For a stochastic Petri net, the size of each species is given by an (evolving) non-negative integer.

The state of the net is therefore given by a triple (s,i,r) of natural numbers. In other words, the state space is \\(\mathbb{N}^3\\).

The transitions fire at random times, and have the effect of decreasing their input populations and increasing their output populations by the indicated amounts.

One firing of recovery has the effect of decreasing \\(I\\) by 1 and increasing \\(R\\) by 1.

Formally, one firing of infection would decrease \\(S\\) and \\(I\\) by, and increase \\(I\\) by 2. But netting this out, we see that one firing of infection decreases \\(S\\) by 1 and increases \\(I\\) by 1.

For example, suppose we were in state \\(x = (5,2,1)\\).

Then if infection fired, we would move to \\(x' = (4,3,1)\\).

Then if recovery fired, we would move to \\(x'' = (4,2,2)\\).

The state of the net is therefore given by a triple (s,i,r) of natural numbers. In other words, the state space is \\(\mathbb{N}^3\\).

The transitions fire at random times, and have the effect of decreasing their input populations and increasing their output populations by the indicated amounts.

One firing of recovery has the effect of decreasing \\(I\\) by 1 and increasing \\(R\\) by 1.

Formally, one firing of infection would decrease \\(S\\) and \\(I\\) by, and increase \\(I\\) by 2. But netting this out, we see that one firing of infection decreases \\(S\\) by 1 and increases \\(I\\) by 1.

For example, suppose we were in state \\(x = (5,2,1)\\).

Then if infection fired, we would move to \\(x' = (4,3,1)\\).

Then if recovery fired, we would move to \\(x'' = (4,2,2)\\).