In the present article, we construct a logarithm transformation based Milstein-type method for the stochastic susceptible-infected-susceptible (SIS) epidemic model evolving in the domain (0,N). The new scheme is explicit and unconditionally boundary and dynamics preserving, when used to solve the stochastic SIS epidemic model. Also, it is proved that the scheme has a strong convergence rate of order one. Different from existing time discretization schemes, the newly proposed scheme for any time step size h > 0, not only produces numerical approximations living in the entire domain (0,N), but also unconditionally reproduces the extinction and persistence behavior of the original model, with no additional requirements imposed on the model parameters. Numerical experiments are presented to verify our theoretical findings.

翻译：本文针对定义在区域(0,N)上的随机易感-感染-易感(SIS)流行病模型，构建了一种基于对数变换的Milstein型数值方法。该新格式在求解随机SIS流行病模型时具有显式特性，且无条件保持边界与动态特性。同时，我们证明了该格式具有一阶强收敛速度。与现有时间离散化格式不同，新提出的格式对于任意步长h>0，不仅能在整个定义域(0,N)内生成数值近似解，而且无需对模型参数附加任何条件即可无条件复现原模型的灭绝与持续行为。数值实验验证了我们的理论结果。