  By combining a logarithm transformation with a corrected Milstein-type
method, the present article proposes an explicit, unconditional boundary and
dynamics preserving scheme for the stochastic susceptible-infected-susceptible
(SIS) epidemic model that takes value in (0,N). The scheme applied to the model
is first proved to have a strong convergence rate of order one. Further, the
dynamic behaviors are analyzed for the numerical approximations and it is shown
that the scheme can unconditionally preserve both the domain and the dynamics
of the model. More precisely, the proposed scheme gives numerical
approximations living in the domain (0,N) and reproducing the extinction and
persistence properties of the original model for any time discretization
step-size h > 0, without any additional requirements on the model parameters.
Numerical experiments are presented to verify our theoretical results.
