The solution [[S == r7, I == 0, R == r8]] should be read as follows: the set of solutions is an infinite two-parameter space, which can be parametrized by two anonymous parameters r7 and r8 that Sage created for the purpose of describing the solution set. Each time you solve a new equation whose set of solutions is huge, Sage will create new symbolic variables to serve as a parameters to describe the solutions set.
The solution [[S == r7, I == 0, R == r8]] should be read as follows: the set of solutions is an infinite two-parameter space, which can be parametrized by two anonymous parameters r7 and r8 that Sage created for the purpose of describing the solution set. Each time you solve a new equation whose set of solutions is huge, Sage will create new symbolic variables parameters (symbolic variables) to serve as a parameters to describe the solutions set.