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Stochastic Dynamics of a Virus Variant Epidemic Model with Double Inoculations

Author

Listed:
  • Hui Chen

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, China
    These authors contributed equally to this work.)

  • Xuewen Tan

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, China
    These authors contributed equally to this work.)

  • Jun Wang

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, China)

  • Wenjie Qin

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, China)

  • Wenhui Luo

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, China)

Abstract

In this paper, we establish a random epidemic model with double vaccination and spontaneous variation of the virus. Firstly, we prove the global existence and uniqueness of positive solutions for a stochastic epidemic model. Secondly, we prove the threshold R 0 * can be used to control the stochastic dynamics of the model. If R 0 * < 0 , the disease will be extinct with probability 1; whereas if R 0 * > 0 , the disease can almost certainly continue to exist, and there is a unique stable distribution. Finally, we give some numerical examples to verify our theoretical results. Most of the existing studies prove the stochastic dynamics of the model by constructing Lyapunov functions. However, the construction of a Lyapunov function of higher-order models is extremely complex, so this method is not applicable to all models. In this paper, we use the definition method suitable for more models to prove the stationary distribution. Most of the stochastic infectious disease models studied now are second-order or third-order, and cannot accurately describe infectious diseases. In order to solve this kind of problem, this paper adopts a higher price five-order model.

Suggested Citation

  • Hui Chen & Xuewen Tan & Jun Wang & Wenjie Qin & Wenhui Luo, 2023. "Stochastic Dynamics of a Virus Variant Epidemic Model with Double Inoculations," Mathematics, MDPI, vol. 11(7), pages 1-29, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1712-:d:1114863
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    References listed on IDEAS

    as
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    4. Yongli Cai & Xixi Wang & Weiming Wang & Min Zhao, 2013. "Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, June.
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    6. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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