Do you mean SIR, where S=number susceptible, I=number infected, R=number recovered (immune)?
S, I, R are functions of time t and dS/dt+dI/dt+dR/dt=0 implying S(t)+I(t)+R(t)=constant at any particular time.
Apparently the differential equation can be applied to various infectious diseases (e.g., measles).
The situation is dynamic, changing in time as people catch the disease through contact and recover from it. Hence the common factor time. The model shows that as the disease spreads the pool of susceptibles decreases as people catch and recover the disease. Once all those susceptible have contracted the disease and recovered, the pool of susceptibles has to be built up again (newborn babies, people coming into the area where the disease is prevalent, etc.).