  In this paper, we are concerned with the stochastic
susceptible-infectious-susceptible (SIS) epidemic model on the complete graph
with $n$ vertices. This model has two parameters, which are the infection rate
and the recovery rate. By utilizing the theory of density-dependent Markov
chains, we give consistent estimations of the above two parameters as $n$ grows
to infinity according to the sample path of the model in a finite time
interval. Furthermore, we establish the central limit theorem (CLT) and the
moderate deviation principle (MDP) of our estimations. As an application of our
CLT, reject regions of hypothesis testings of two parameters are given. As an
application of our MDP, confidence intervals with lengths converging to $0$
while confidence levels converging to $1$ are given as $n$ grows to infinity.
