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Analysing Social Epidemics by Delayed Stochastic Models

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  • Francisco-José Santonja
  • Leonid Shaikhet

Abstract

We investigate the dynamics of a delayed stochastic mathematical model to understand the evolution of the alcohol consumption in Spain. Sufficient condition for stability in probability of the equilibrium point of the dynamic model with aftereffect and stochastic perturbations is obtained via Kolmanovskii and Shaikhet general method of Lyapunov functionals construction. We conclude that alcohol consumption in Spain will be constant (with stability) in time with around 36.47% of nonconsumers, 62.94% of nonrisk consumers, and 0.59% of risk consumers. This approach allows us to emphasize the possibilities of the dynamical models in order to study human behaviour.

Suggested Citation

  • Francisco-José Santonja & Leonid Shaikhet, 2012. "Analysing Social Epidemics by Delayed Stochastic Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-13, July.
    • Handle: RePEc:hin:jnddns:530472
    DOI: 10.1155/2012/530472
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    Cited by:

    1. Juan Carlos Cortés & Marc Jornet, 2020. "L p -Solution to the Random Linear Delay Differential Equation with a Stochastic Forcing Term," Mathematics, MDPI, vol. 8(6), pages 1-16, June.

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