Research article Special Issues

Global stability of a multi-group delayed epidemic model with logistic growth

  • Received: 07 February 2023 Revised: 29 May 2023 Accepted: 02 July 2023 Published: 19 July 2023
  • MSC : 37N25, 92C42

  • In this work, we aim to investigate the mechanism of a multi-group epidemic model taking into account the influences of logistic growth and delay time distribution. Despite the importance of the logistic growth effect in such models, its consideration remains rare. We show that $ \mathcal{R}_0 $ has a crusher role in the global stability of a disease-free and endemic equilibria. That is, if $ \mathcal{R}_0 $ is less than or equal to one, then the disease-free equilibrium is globally asymptotically stable, whereas, if $ \mathcal{R}_0 $ is greater than one, then a unique endemic equilibrium exists and is globally asymptotically stable. In addition, we construct suitable Lyapunov functions to investigate the global stability of disease-free and endemic equilibria. Finally, we introduce numerical simulations of the model.

    Citation: B. M. Almuqati, F. M. Allehiany. Global stability of a multi-group delayed epidemic model with logistic growth[J]. AIMS Mathematics, 2023, 8(10): 23046-23061. doi: 10.3934/math.20231173

    Related Papers:

  • In this work, we aim to investigate the mechanism of a multi-group epidemic model taking into account the influences of logistic growth and delay time distribution. Despite the importance of the logistic growth effect in such models, its consideration remains rare. We show that $ \mathcal{R}_0 $ has a crusher role in the global stability of a disease-free and endemic equilibria. That is, if $ \mathcal{R}_0 $ is less than or equal to one, then the disease-free equilibrium is globally asymptotically stable, whereas, if $ \mathcal{R}_0 $ is greater than one, then a unique endemic equilibrium exists and is globally asymptotically stable. In addition, we construct suitable Lyapunov functions to investigate the global stability of disease-free and endemic equilibria. Finally, we introduce numerical simulations of the model.



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