Global stability of discrete virus dynamics models with humoural immunity and latency

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. ARTICLE HISTORY

A dynamically-consistent nonstandard finite difference scheme for the SICA model

“…Individuals infected with HIV are more likely to develop tuberculosis because of their immunodeficiency, so a model that considers HIV and tuberculosis is very interesting to investigate. One can find many studies in the literature [1][2][3]. A TB-HIV/AIDS co-infection model, that contains the celebrated SICA arXiv:2105.10826v2 [math.NA] 27 May 2021 (Susceptible-Infected-Chronic-AIDS) model as a sub-model, was first proposed in [4]:…”

Discrete-Time System of an Intracellular Delayed HIV Model with CTL Immune Response

“…where the denominator function is φ(h) = h [7,14]. Throughout our study, for brevity, we write φ(h) = φ.…”

“…In [5], it is assumed that CTL proliferation depends, besides infected cells, as usual, also on healthy cells. Recently, the same problem was tackled by introducing time delays [7,19], which is justified by the fact that uninfected cells must be in contact with the HIV virus before they become infected. In [1], the investigation continued and the proposed basic model, illustrating this type of scenario, is…”

Global Properties of a Discrete SARS-CoV-2/HIV Co-Dynamics Model

“…Coronavirus disease 2019 (COVID- 19), a new epidemic that surfaced in late 2019 in China, is a respiratory illness caused by a virus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). SARS-CoV-2 is indeed an RNA virus, and it belongs to the Coronaviridae family [1].…”