Author:
Almuqati B. M.,Allehiany F. M.
Abstract
<abstract><p>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.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference31 articles.
1. D. J. Daley, J. Gani, Epidemic modelling: An introduction, Cambridge: Cambridge University Press, 2001.
2. W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond. Ser. A, 115 (1927), 700–721. https://doi.org/10.1098/rspa.1927.0118
3. F. Brauer, C. Castillo-Chavez, Mathematical models in population biology and epidemiology, In: Texts in applied mathematics, New York: Springer New York, 2012. https://doi.org/10.1007/978-1-4614-1686-9
4. Z. Ma, Dynamical modeling and analysis of epidemics, World Scientific, 2009.
5. E. Beretta, T. Hara, W. B. Ma, Y. Takeuchi, Global asymptotic stability of an SIR epidemic model with distributed time delay, Nonlinear Anal., 47 (2001), 4107–4115.