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A Stochastic Semi-Parametric SEIR Model with Infectivity in an Incubation Period

Author

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  • Jing Zhang

    (School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China)

  • Tong Jin

    (School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China)

Abstract

This paper introduces stochastic disturbances into a semi-parametric SEIR model with infectivity in an incubation period. The model combines the randomness of disease transmission and the nonlinearity of transmission rate, providing a flexible framework for more accurate description of the process of infectious disease transmission. On the basis of the discussion of the deterministic model, the stochastic semi-parametric SEIR model is studied. Firstly, we use Lyapunov analysis to prove the existence and uniqueness of global positive solutions for the model. Secondly, the conditions for disease extinction are established, and appropriate stochastic Lyapunov functions are constructed to discuss the asymptotic behavior of the model’s solution at the disease-free equilibrium point of the deterministic model. Finally, the specific transmission functions are enumerated, and the accuracy of the results are demonstrated through numerical simulations.

Suggested Citation

  • Jing Zhang & Tong Jin, 2024. "A Stochastic Semi-Parametric SEIR Model with Infectivity in an Incubation Period," Mathematics, MDPI, vol. 12(10), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1580-:d:1397237
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    References listed on IDEAS

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    1. Naim, Mouhcine & Lahmidi, Fouad & Namir, Abdelwahed & Kouidere, Abdelfatah, 2021. "Dynamics of an fractional SEIR epidemic model with infectivity in latent period and general nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Feng Wang & Shan Wang & Youhua Peng, 2020. "Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-12, May.
    3. Piovella, Nicola, 2020. "Analytical solution of SEIR model describing the free spread of the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. 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.
    5. Wei, Fengying & Xue, Rui, 2020. "Stability and extinction of SEIR epidemic models with generalized nonlinear incidence," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 1-15.
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