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A stochastic SIS model driven by random diffusion of air pollutants

Author

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  • He, Sha
  • Tang, Sanyi
  • Wang, Weiming

Abstract

In this paper, a stochastic SIS model related to respiratory disease driven by random diffusion of air pollutants has been developed, in which the transmission coefficient is a function of air quality index. By applying the statistical properties of stochastic process, we derive a one-dimensional stochastic differential equation (SDE) model for the number of infected individuals. Then we show the existence and uniqueness of positive solution of the SDE model. Moreover, the critical conditions that guarantee the persistence and extinction have been obtained, meanwhile the results reveal that strong noise intensity will make the disease extinct instead. In fact, we find that the random fluctuation of the original two-dimensional coupling model and the reduced model are different by comparing their sample paths. The corresponding images of power spectral densities related to real data and the two models further illustrate this phenomenon. Finally, uncertainty and sensitivity analyses reveal that the parameters related to air pollution have great influence on the critical condition and dynamics of the proposed model.

Suggested Citation

  • He, Sha & Tang, Sanyi & Wang, Weiming, 2019. "A stochastic SIS model driven by random diffusion of air pollutants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    • Handle: RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119310064
    DOI: 10.1016/j.physa.2019.121759
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    Citations

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    Cited by:

    1. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Zhou, Qi & Li, Xining & Hu, Jing & Zhang, Qimin, 2024. "Dynamics and optimal control for a spatial heterogeneity model describing respiratory infectious diseases affected by air pollution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 276-295.
    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. 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.
    5. Lu, Chun, 2021. "Dynamics of a stochastic Markovian switching predator–prey model with infinite memory and general Lévy jumps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 316-332.
    6. Xinhai Lu & Yanwei Zhang & Handong Tang, 2021. "Modeling and Simulation of Dissemination of Cultivated Land Protection Policies in China," Land, MDPI, vol. 10(2), pages 1-21, February.

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