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A stochastic SIHR epidemic model with general population-size dependent contact rate and Ornstein–Uhlenbeck process: dynamics analysis

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Abstract

The purpose of this work is to investigate a novel stochastic SIHR epidemic model, which includes a general incidence rate and mean-reversion Ornstein–Uhlenbeck process. Firstly, the existence of global positivity of the solution is testified by Lyapunov function. Secondly, this disease will be eradicated if the reproduction number \(\mathcal {R}_{0}^{s}<1\). Otherwise, if the reproduction number \(\mathcal {R}_{0}^{*}>1\), then the system has a stationary distribution, which means that the pandemic will persist. In addition, an explicit expression of the probability density function for a linear system near quasi-endemic equilibrium is obtained under certain conditions. Finally, a series of numerical simulations is carried out to validate the theoretical conclusions.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The work is supported by the National Natural Science Foundation of China (Nos. 11671236, 11871473) and the Fundamental Research Funds for the Central Universities, China (Nos. 22CX03013A, 22CX03030A).

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Authors and Affiliations

  1. School of Management Science, Qufu Normal University, Rizhao, 276800, Shandong, China

    Xiaojie Mu

  2. College of Science, China University of Petroleum (East China), Qingdao, 266580, Shandong, China

    Daqing Jiang

Authors
  1. Xiaojie Mu
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  2. Daqing Jiang
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Contributions

XM: Software, Validation, Formal analysis, Investigation, Data curation, Writing-original draft, Writing-review & editing. DJ: Conceptualization, Methodology, Validation, Formal analysis, Visualization, Supervision, Funding acquisition.

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Correspondence to Daqing Jiang.

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Mu, X., Jiang, D. A stochastic SIHR epidemic model with general population-size dependent contact rate and Ornstein–Uhlenbeck process: dynamics analysis. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09586-9

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