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Dynamics of a Stochastic SEIR Epidemic Model with Vertical Transmission and Standard Incidence

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  • Ruichao Li

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Xiurong Guo

    (Department of Basic Courses, Shandong University of Science and Technology, Tai’an 271019, China)

Abstract

A stochastic SEIR epidemic model with standard incidence and vertical transmission was developed in this work. The primary goal of this study was to determine whether stochastic environmental disturbances affect dynamic features of the epidemic model. The existence, uniqueness, and boundedness of global positive solutions are stated. A threshold was determined for the extinction of the infectious disease. After that, the existence and uniqueness of an ergodic stationary distribution were verified by determining the correct Lyapunov function. Ultimately, theoretical outcomes of numerical simulations are shown.

Suggested Citation

  • Ruichao Li & Xiurong Guo, 2024. "Dynamics of a Stochastic SEIR Epidemic Model with Vertical Transmission and Standard Incidence," Mathematics, MDPI, vol. 12(3), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:359-:d:1324429
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    References listed on IDEAS

    as
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    2. Qi, Haokun & Meng, Xinzhu, 2021. "Mathematical modeling, analysis and numerical simulation of HIV: The influence of stochastic environmental fluctuations on dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 700-719.
    3. Huyi Wang & Ge Zhang & Tao Chen & Zhiming Li, 2023. "Threshold Analysis of a Stochastic SIRS Epidemic Model with Logistic Birth and Nonlinear Incidence," Mathematics, MDPI, vol. 11(7), pages 1-17, April.
    4. Jin, Xihua & Jia, Jianwen, 2020. "Qualitative study of a stochastic SIRS epidemic model with information intervention," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    5. Xuan Leng & Asad Khan & Anwarud Din, 2023. "Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    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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    Cited by:

    1. Zhixian Zhang & Xiaoquan Ding, 2025. "Dynamics of a Stochastic Single-Species Kolmogorov System Under Markovian Switching," Mathematics, MDPI, vol. 13(5), pages 1-13, February.

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