AI 中文总结
提出并分析由时变布朗运动驱动的扩散时变随机SIS传染病模型，证明其全局正解唯一性，探究疾病灭绝与持久性，构造保正对数欧拉-丸山数值方法并证明强收敛阶，通过数值实验验证收敛率与保正性。
AI 中文摘要
本文提出并分析了一类由时变布朗运动驱动的扩散时间变换易感-感染-易感（SIS）传染病模型。我们证明，对于$(0,N)$中的任意初值，所提模型存在唯一的全局正解。随后探究了疾病的灭绝性与持久性。为逼近该扩散时间变换SIS模型，我们构造了一种保正的对数欧拉-丸山（LEM）方法。假设时间变换由满足$α\in(0,1)$的标准$α$稳定从属过程的逆给出，我们证明数值解以$α$阶强收敛于精确解。最后，通过数值实验验证了理论预测的收敛阶，并阐明了所提方法的保正性。
英文摘要
In this paper, we propose and analyze a diffusion time-changed susceptible-infected-susceptible (SIS) epidemic model driven by time-changed Brownian motion. We prove that the proposed model admits a unique global positive solution for any initial value in $(0,N)$. The extinction and persistence of the disease are then investigated. To approximate the diffusion time-changed SIS model, we construct a positivity-preserving logarithmic Euler-Maruyama (LEM) method. Assuming that the time-changed is given by the inverse of a standard $α$-stable subordinator with $α\in(0,1)$, we prove that the numerical solution converges strongly to the exact solution with order $α$. Finally, numerical experiments are provided to confirm the predicted convergence rates and illustrate the positivity-preserving property of the proposed method.
Comments17 pages, 4 figures
