Take for instance the following model describing an epedemic accounting for the number of susceptible people $S$ and the number of infected people $I$ $$\frac{dS(t)}{dt} = -aS(t) \cdot I(t)$$ $$\frac{dI(t)}{dt}=aS(t) \cdot I(t) - bI(t)$$, where $a,b>0$
What are the reasons that models like this are very often described by ODE's rather than just describing them as regular functions, i.e look at the development of $S(t)$ and $I(t)$? \
After all, aren't we interested in knowing about the number of people in the different states? Using ODE's just seems to complicate matters.