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Published in: Journal of Applied Mathematics and Computing 1-2/2021

12-02-2021 | Original Research

Asymptotic behavior of a discrete-time density-dependent SI epidemic model with constant recruitment

Authors: M. R. S. KulenoviĆ, M. NurkanoviĆ, Abdul-Aziz Yakubu

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2021

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Abstract

We use the epidemic threshold parameter, \({{\mathcal {R}}}_{0}\), and invariant rectangles to investigate the global asymptotic behavior of solutions of the density-dependent discrete-time SI epidemic model where the variables \(S_{n}\) and \(I_{n}\) represent the populations of susceptibles and infectives at time \(n = 0,1,\ldots \), respectively. The model features constant survival “probabilities” of susceptible and infective individuals and the constant recruitment per the unit time interval \([n, n+1]\) into the susceptible class. We compute the basic reproductive number, \({{\mathcal {R}}}_{0}\), and use it to prove that independent of positive initial population sizes, \({{\mathcal {R}}}_{0}<1\) implies the unique disease-free equilibrium is globally stable and the infective population goes extinct. However, the unique endemic equilibrium is globally stable and the infective population persists whenever \({{\mathcal {R}}}_{0}>1\) and the constant survival probability of susceptible is either less than or equal than 1/3 or the constant recruitment is large enough.

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Metadata
Title
Asymptotic behavior of a discrete-time density-dependent SI epidemic model with constant recruitment
Authors
M. R. S. KulenoviĆ
M. NurkanoviĆ
Abdul-Aziz Yakubu
Publication date
12-02-2021
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 1-2/2021
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-021-01503-2

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