Global dynamics of alcoholism epidemic model with distributed delays

Salih Djillali, Soufiane Bentout, Tarik Mohammed Touaoula, Abdessamad Tridane

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


This paper aims to investigate the global dynamics of an alcoholism epidemic model with distributed delays. The main feature of this model is that it includes the effect of the social pressure as a factor of drinking. As a result, our global stability is obtained without a "basic reproduction number" nor threshold condition. Hence, we prove that the alcohol addiction will be always uniformly persistent in the population. This means that the investigated model has only one positive equilibrium, and it is globally asymptotically stable independent on the model parameters. This result is shown by proving that the unique equilibrium is locally stable, and the global attraction is shown using Lyapunov direct method.

Original languageEnglish
Pages (from-to)8245-8256
Number of pages12
JournalMathematical Biosciences and Engineering
Issue number6
Publication statusPublished - 2021


  • Alcoholism model
  • Global stability
  • Lyapunov direct method

ASJC Scopus subject areas

  • Modelling and Simulation
  • General Agricultural and Biological Sciences
  • Computational Mathematics
  • Applied Mathematics


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