Global stability for a delayed HIV reactivation model with latent infection and Beddington–DeAngelis incidence

Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response

“…This subsection computes all steady states of system (5) – (10) and the threshold parameters that guarantee the existence of these steady states. For system (5) – (10) we define the basic reproduction number as [51] : For convenience, let . Then, can be rewritten as: Let be any steady state of system (5) – (10) satisfying the following system of equations: By solving system (14) – (19) , we get five steady states:…”

“…These model assumed that one infected, the cell immediately becomes a latent infected cell. Further, these models neglected the time for the latent infected cells to be activated [51] . Furthermore, the maturation time of the new viruses was not considered.…”

Global stability for an endogenous-reactivated tuberculosis model with Beddington-DeAngelis incidence, distributed delay and relapse

“…Baba [30] presented a TB epidemic model with saturated incidence, showed that effective control strategies would give rise to a reduction of infectious population. Additionally, the Beddington-DeAngelis incidence function βSI 1+ηsS+η I I containing the inhibitory effect of susceptible and infectious individuals, has been gradually employed in epidemic models [21,24], which could include the bilinear incidence function βSI (η s = 0, η I = 0) and saturated incidence function βSI 1+η I I (η s = 0) as special cases. Furthermore, time delays are normally used to describe a required time period for an individual from infection to be infectious [31].…”

“…As well known, incidence function performs a vital role in epidemic models to characterize the interaction between susceptible and infectious individuals, and usually includes bilinear and non-linear incidences etc. [20], in which nonlinear incidences such as saturated, ratio-dependent and Beddington-DeAngelis incidences have been proven that are more appropriate and exact to describe the complicated interactive course of disease transmission [21][22][23][24][25]. However, most TB epidemic models usually used bilinear [6,13,14,26] and standard incidences [12,27,28], while very few considered non-linear incidence.…”

Global stability of a delayed SARS-CoV-2 reactivation model with logistic growth, antibody immunity and general incidence rate

“…The models presented in [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] assumed that one infected, the cell immediately becomes a latent infected cell. Further, these models neglected the time for the latent infected cells to be activated [45] . Furthermore, the maturation time of the new viruses was not considered.…”