  Threshold theorem is probably the most important development of mathematical
epidemic modelling. Unfortunately, some models may not behave according to the
threshold. In this paper, we will focus on the final outcome of SIR model with
demography. The behaviour of the model approached by deteministic and
stochastic models will be introduced, mainly using simulations. Furthermore, we
will also investigate the dynamic of susceptibles in population in absence of
infective. We have successfully showed that both deterministic and stochastic
models performed similar results when $R_0 \leq 1$. That is, the disease-free
stage in the epidemic. But when $R_0 > 1$, the deterministic and stochastic
approaches had different interpretations.
