#### Title

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

#### Document Type

Article

#### Date of Original Version

1-1-2021

#### Abstract

We use the epidemic threshold parameter, R, and invariant rectangles to investigate the global asymptotic behavior of solutions of the density-dependent discrete-time SI epidemic model where the variables Sn and In represent the populations of susceptibles and infectives at time n= 0 , 1 , … , 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, R, and use it to prove that independent of positive initial population sizes, R< 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 R> 1 and the constant survival probability of susceptible is either less than or equal than 1/3 or the constant recruitment is large enough.

#### Publication Title

Journal of Applied Mathematics and Computing

#### Citation/Publisher Attribution

KulenoviĆ, M. R., M. NurkanoviĆ, and Abdul A. Yakubu.
"Asymptotic behavior of a discrete-time density-dependent SI epidemic model with constant recruitment."
*Journal of Applied Mathematics and Computing*
,
(2021).
doi:10.1007/s12190-021-01503-2.