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Global behaviour of a class of discrete epidemiological SI models with constant recruitment of susceptibles.
- Source :
-
Journal of Difference Equations & Applications . Feb2022, Vol. 28 Issue 2, p259-288. 30p. - Publication Year :
- 2022
-
Abstract
- Motivated by the recent paper [M.R.S. Kulenović, M. Nurkanović, and A.A. Yakubu, Asymptotic behaviour of a discrete-time density-dependent SI epidemic model with constant recruitment, J. Appl. Math. Comput. 67 (2021), pp. 733–753. DOI:], in this paper, we consider the class of the SI epidemic models with recruitment where the Poisson function, a decreasing exponential function of the population of infectious individuals, is replaced by a general probability function that satisfies certain conditions. We compute the basic reproduction number R 0. We establish the global asymptotic stability of the disease-free equilibrium (GAS) for R 0 < 1. We use the Lyapunov function method developed in [P. van den Driessche and A.-A. Yakubu, Disease extinction versus persistence in discrete-time epidemic models, Bull. Math. Biol. 81 (2019), pp. 4412–4446], to demonstrate the GAS of the disease-free equilibrium and uniform persistence of the considered class of models. We show that the considered type of model is permanent for R 0 > 1. For R 0 = 1 , the transcritical bifurcation appears. For R 0 > 1 , we prove the global attractivity result for endemic equilibrium and instability of the disease-free equilibrium. We apply theoretical results to specific escape functions of the susceptibles from infectious individuals. For each case, we compute the basic reproduction number R 0 . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10236198
- Volume :
- 28
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Difference Equations & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 155832618
- Full Text :
- https://doi.org/10.1080/10236198.2022.2042277