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Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model

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Abstract

This paper aims to establish a novel explicit method for the stochastic SIS epidemic model, which can preserve the bounded positive domain and asymptotic properties. The proposed new method is based on combining a logarithmic transformation with a truncated Euler-Maruyama method, and it has the first-order rate of convergence for the pth-moment with \(p>0\). Moreover, without additional restriction conditions except those necessary to guarantee the extinction of the exact solution, the approximation of the extinction is achieved for the stochastic SIS model whose coefficients violate the global monotonicity condition. Some numerical experiments are given to illustrate the theoretical results and testify to the efficiency of our algorithm.

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Acknowledgements

The authors thank the associated editor and anonymous reviewers for the helpful comments and suggestions.

Funding

The research of Hongfu Yang was supported by the Natural Science Foundation of Guangxi Province (Nos. 2023GXNSFFA026001, 2023GXNSFAA026246, 2021GXNSFBA196080, Guike AD21220062), the National Natural Science Foundation of China (Nos. 11971096, 12101144, 62241303), the High-level Talent Project of Guangxi Normal University (2022TD003), the Guangxi Basic Ability Promotion Project for Young and Middle-aged Teachers (2023KY0067), and the Fundamental Research Funds for the Central Universities. The research of Jianhua Huang was supported by the National Natural Science Foundation of China (No. 12031020).

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Authors and Affiliations

  1. College of Science, National University of Defense Technology, Changsha, 410073, Hunan, China

    Hongfu Yang & Jianhua Huang

  2. School of Mathematics and Statistics, Guangxi Normal University, Guilin, 541004, Guangxi, China

    Hongfu Yang

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  1. Hongfu Yang
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  2. Jianhua Huang
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Contributions

Hongfu Yang: methodology, formal analysis, writing—original draft, writing—review and editing, software, supervision, funding acquisition. Jianhua Huang: methodology, formal analysis, writing—original draft, writing—review and editing, software, supervision, funding acquisition.

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Correspondence to Hongfu Yang or Jianhua Huang.

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Yang, H., Huang, J. Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model. Numer Algor 95, 1475–1502 (2024). https://doi.org/10.1007/s11075-023-01617-7

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