  Studies about epidemic modelling have been conducted since before 19th
century. Both deterministic and stochastiic model were used to capture the
dynamic of infection in the population. The purpose of this project is to
investigate the behaviour of the models when we set the basic reproduction
number, $R_0$. This quantity is defined as the expected number of contacts made
by a typical infective to susceptibles in the population. According to the
epidemic threshold theory, when $R_0 \leq 1$, minor epidemic occurs with
probability one in both approaches, but when $R_0 > 1$, the deterministic and
stochastic models have different interpretation. In the deterministic approach,
major epidemic occurs with probability one when $R_0 > 1$ and predicts that the
disease will settle down to an endemic equilibrium. Stochastic models, on the
other hand, identify that the minor epidemic can possibly occur. If it does,
then the epidemic will die out quickly. Moreover, if we let the population size
be large and the major epidemic occurs, then it will take off and then reach
the endemic level and move randomly around the deterministic's equilibrium.
