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Stationary distribution and probability density for a stochastic SEIR-type model of coronavirus (COVID-19) with asymptomatic carriers

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  • Liu, Qun
  • Jiang, Daqing

Abstract

In this paper, we propose a stochastic SEIR-type model with asymptomatic carriers to describe the propagation mechanism of coronavirus (COVID-19) in the population. Firstly, we show that there exists a unique global positive solution of the stochastic system with any positive initial value. Then we adopt a stochastic Lyapunov function method to establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the stochastic model. Especially, under the same conditions as the existence of a stationary distribution, we obtain the specific form of the probability density around the quasi-endemic equilibrium of the stochastic system. Finally, numerical simulations are introduced to validate the theoretical findings.

Suggested Citation

  • Liu, Qun & Jiang, Daqing, 2023. "Stationary distribution and probability density for a stochastic SEIR-type model of coronavirus (COVID-19) with asymptomatic carriers," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001571
    DOI: 10.1016/j.chaos.2023.113256
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    References listed on IDEAS

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    1. Ye Wang & Thabet Abdeljawad & Anwarud Din, 2022. "Modeling The Dynamics Of Stochastic Norovirus Epidemic Model With Time Delay," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-13, August.
    2. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing, 2021. "Ergodic property, extinction and density function of a stochastic SIR epidemic model with nonlinear incidence and general stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Lu, Minmin & Wang, Yan & Jiang, Daqing, 2021. "Stationary distribution and probability density function analysis of a stochastic HIV model with cell-to-cell infection," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    4. Zhu, Yu & Wang, Liang & Qiu, Zhipeng, 2022. "Dynamics of a stochastic cholera epidemic model with Lévy process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    5. Rathinasamy, A. & Chinnadurai, M. & Athithan, S., 2021. "Analysis of exact solution of stochastic sex-structured HIV/AIDS epidemic model with effect of screening of infectives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 213-237.
    6. Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution and extinction of a stochastic staged progression AIDS model with staged treatment and second-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Ge, Junyan & Zuo, Wenjie & Jiang, Daqing, 2022. "Stationary distribution and density function analysis of a stochastic epidemic HBV model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 232-255.
    8. Han, Bingtao & Zhou, Baoquan & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary solution, extinction and density function for a high-dimensional stochastic SEI epidemic model with general distributed delay," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    9. Zhou, Baoquan & Jiang, Daqing & Han, Bingtao & Hayat, Tasawar, 2022. "Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 15-44.
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    1. Saha, Pritam & Mondal, Bapin & Ghosh, Uttam, 2023. "Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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