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Stationary distribution and extinction of a stochastic model of syphilis transmission in an MSM population with telegraph noises

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Abstract

This paper is concerned with the dynamical behaviors of a model of syphilis transmission disturbed by both white noises and telegraph noises. Multiple infections and treatment stages are considered, which include and extend the existing ones. The existence and ergodicity of the stationary distribution are obtained by constructing a suitable Lyapunov function, which determines a critical value \(R_0^*\) corresponding to the control reproduction number \(R_c\) of the corresponding determined system. In addition, a sufficient criteria for extinction of the diseases is derived. Finally, the numerical simulations illustrate our theoretical results, which show that, the stronger white noises can result in the extinction of the diseases and telegraph noises can strength the stability of the system.

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Acknowledgements

The work is supported by the NSFC of China (Nos. 11671236, 11871473) and Shandong Provincial Natural Science Foundation (Nos. ZR2019MA006, ZR2019MA010), and the Fundamental Research Funds for the Central Universities (No. 19CX02055A).

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Authors and Affiliations

  1. College of Science, China University of Petroleum (East China), Qingdao, 266580, People’s Republic of China

    Yaxin Zhou, Wenjie Zuo, Daqing Jiang & Mingyu Song

  2. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University, Jeddah, Saudi Arabia

    Daqing Jiang

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  1. Yaxin Zhou
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  2. Wenjie Zuo
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Correspondence to Wenjie Zuo.

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Zhou, Y., Zuo, W., Jiang, D. et al. Stationary distribution and extinction of a stochastic model of syphilis transmission in an MSM population with telegraph noises. J. Appl. Math. Comput. 66, 645–672 (2021). https://doi.org/10.1007/s12190-020-01453-1

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