School of Mathematics, Harbin Institute of Technology, Harbin, P.R. China.
J Comput Biol. 2023 Oct;30(10):1098-1111. doi: 10.1089/cmb.2022.0462. Epub 2023 Oct 9.
This article deals with the numerical positivity, boundedness, convergence, and dynamical behaviors for stochastic susceptible-infected-susceptible (SIS) model. To guarantee the biological significance of the split-step backward Euler method applied to the stochastic SIS model, the numerical positivity and boundedness are investigated by the truncated Wiener process. Motivated by the almost sure boundedness of exact and numerical solutions, the convergence is discussed by the fundamental convergence theorem with a local Lipschitz condition. Moreover, the numerical extinction and persistence are initially obtained by an exponential presentation of the stochastic stability function and strong law of the large number for martingales, which reproduces the existing theoretical results. Finally, numerical examples are given to validate our numerical results for the stochastic SIS model.
本文研究了随机 SIS 模型的数值正定性、有界性、收敛性和动力学行为。为了保证应用于随机 SIS 模型的分步向后 Euler 方法的生物学意义，通过截断 Wiener 过程研究了数值正定性和有界性。受精确和数值解的几乎必然有界性的启发，利用局部 Lipschitz 条件的基本收敛定理讨论了收敛性。此外，通过鞅的随机稳定性函数和大数定律的指数表示，最初得到了数值灭绝和持久性，这再现了现有的理论结果。最后，给出了数值示例来验证我们对随机 SIS 模型的数值结果。
