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On the Stochastic Dynamics of a Social Epidemics Model

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  • Xun-Yang Wang
  • Peng-Zhan Zhang
  • Qing-Shan Yang

Abstract

Alcohol abuse is a major social problem, which has caused a lot of damages or hidden dangers to the individual and the society. In this paper, with random factors of alcoholism considered in mortality rate of compartment populations, we formulate a stochastic alcoholism model according to compartment theory of infectious disease. Based on this model, we investigate the long-term stochastic dynamics behaviors of two equilibria of the corresponding deterministic model and point out the effect of random disturbance on the stability of the system. We find that when , we get the estimation between the trajectory of stochastic system and in the average in time with respect to the disturbance intensity, while when , stochastic system is ergodic and has the unique stationary distribution. Finally, we carry out numerical simulations to support the corresponding theoretical results.

Suggested Citation

  • Xun-Yang Wang & Peng-Zhan Zhang & Qing-Shan Yang, 2017. "On the Stochastic Dynamics of a Social Epidemics Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-14, January.
    • Handle: RePEc:hin:jnddns:6297074
    DOI: 10.1155/2017/6297074
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    Cited by:

    1. Zhang, Zili, 2022. "Vibration suppression of floating offshore wind turbines using electromagnetic shunt tuned mass damper," Renewable Energy, Elsevier, vol. 198(C), pages 1279-1295.

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