
SIR epidemic Model
For this model you have the following three equations.
$\displaystyle dS/dt=BSI$
$\displaystyle dI/dt=BSIvI$
$\displaystyle dR/dt=vI$
S` is the number of Susceptibles a time t
I` is the number of Infectives at time t
R` is the number who have recovered at time t
B is the disease transmission rate
v is the recovery rate
My question is, if the population is to be assumed constant, why can you neglect the third equation?

You wrote "... if the population is to be assumed constant ..."
but there is no definition of population.
If population is P=S+I+R=const then
dP/dt=dS/dt+dI/dt+dR/dt=0 and dR/dt may be found to be
dR/dt=dS/dtdI/dt.
Or there is another definition of population?