Global stability of discrete virus dynamics models with humoural immunity and latency. (1st January 2019)

• Record Type: Journal Article
• Authors: Elaiw, A. M.; Alshaikh, M. A.
• Is Part Of: Journal of biological dynamics. Volume 13(2019)Supplement 1
• Page Start: 639
• Page End: 674
• Publication Date: 2019-01-01
• Subjects: Viral infection -- humoural immune response -- latency -- global stability -- discrete-time models -- Lyapunov function; 34D23 -- 93D20 -- 37C75 -- 93D05 -- 93C55; Biology -- Mathematical models -- Periodicals; 570.15118
• DOI: 10.1080/17513758.2019.1683630
• Languages: English
• ISSNs: 1751-3758

Abstract

Abstract : This paper studies the global stability of discrete-time viral infection models with humoural immunity. We consider both latently and actively infected cells. We study also a model with general production and clearance rates of all compartments as well as general incidence rate of infection. We use nonstandard finite difference method to discretize the continuous-time models. The positivity and boundedness of solutions of the discrete models are established. We establish by using Lyapunov method, the global stability of equilibria in terms of the basic reproduction number R 0 and the humoural immune response activation number R 1 . The results signify that the infection dies out if R 0 ≤ 1 . Moreover, the infection persists with inactive immune response if R 1 ≤ 1 < R 0 and with active immune response if R 1 > 1 . We illustrate our theoretical results by using numerical simulations.