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Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model

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Abstract

The paper deals with the numerical positivity, convergence and dynamical behaviors (including extinction and persistence) for stochastic SIS model. Compared with the existing numerical methods, a linearly backward Euler method with truncated Wiener process is introduced with a less computational cost and a better dynamic behavior. We discuss the numerical positivity by the truncated Wiener process, which is the basis for the investigation of convergence and dynamic behavior. The numerical dynamical behaviors (extinction and persistence) are obtained by an exponential representation for the nonlinear stochastic stability function and the large number theorem for martingale, which reproduces the existing theoretical results of exact solution. Finally, numerical examples are given to validate our numerical results for stochastic SIS model.

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Acknowledgements

The authors would like to express their gratitude to the reviewers: their valuable comments and suggestions led to a greatly improved version of the paper.

Funding

This research was supported by the National Natural Science Foundation of China (NSFC 11871179 and NSFC 11771128).

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Authors and Affiliations

  1. School of Mathematics, Harbin Institute of Technology, Harbin, China

    Xiaochen Yang, Mengna Li, Zhanwen Yang & Chiping Zhang

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  1. Xiaochen Yang
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  2. Mengna Li
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Correspondence to Zhanwen Yang.

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Yang, X., Li, M., Yang, Z. et al. Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model. Numer Algor 93, 563–579 (2023). https://doi.org/10.1007/s11075-022-01427-3

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  • DOI: https://doi.org/10.1007/s11075-022-01427-3

Keywords

Mathematics Subject Classification (2010)