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.

翻译：通过将对数变换与修正的Milstein型方法相结合，本文针对取值于(0,N)的随机易感-感染-易感(SIS)传染病模型，提出了一种显式、无条件边界与动力学保持格式。首先证明该格式应用于模型时具有一阶强收敛速度。进一步，对数值近似的动力学行为进行分析，表明该格式能无条件保持模型的域与动力学特性。更精确地说，所提出的格式生成的数值近似严格位于域(0,N)内，且能在任意时间离散步长h>0下复现原始模型的灭绝与持续性质，无需对模型参数施加额外限制。通过数值实验验证了理论结果。