Dynamical Properties of Discrete-Time HTLV-I and HIV-1 within-Host Coinfection Model

Abstract

Infection with human immunodeficiency virus type 1 (HIV-1) or human T-lymphotropic virus type I (HTLV-I) or both can lead to mortality. CD4+T cells are the target for both HTLV-I and HIV-1. In addition, HIV-1 can infect macrophages. CD4+T cells and macrophages play important roles in the immune system response. This article develops and analyzes a discrete-time HTLV-I and HIV-1 co-infection model. The model depicts the within-host interaction of six compartments: uninfected CD4+T cells, HIV-1-infected CD4+T cells, uninfected macrophages, HIV-1-infected macrophages, free HIV-1 particles and HTLV-I-infected CD4+T cells. The discrete-time model is obtained by discretizing the continuous-time model via the nonstandard finite difference (NSFD) approach. We show that NSFD preserves the positivity and boundedness of the model’s solutions. We deduce four threshold parameters that control the existence and stability of the four equilibria of the model. The Lyapunov method is used to examine the global stability of all equilibria. The analytical findings are supported via numerical simulation. The model can be useful when one seeks to design optimal treatment schedules using optimal control theory.

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

“…Mickens [11] introduced a nonstandard finite difference (NSFD) scheme for solving differential equations, which has been effectively applied to various models for within-host viral mono-infection in references [12]- [21]. Furthermore, in [22] and [23],…”

Stabilization Control for a Class of Fractional-Order HIV-1 Infection Model with Time Delays

“…Long-term infection of HIV-1 will cause the failure of the CD4+ T cell bank, then affect the immune response of the body, and finally form acquired immunodeficiency syndrome [7,8]. The establishment of a dynamic model of HIV-1 infection based on HIV-1 can effectively inhibit the spread of infectious diseases and lay a foundation for an in-depth understanding of the virus content in the human body and its evolution over time [9,10]. The study of this dynamic characteristic is of great significance for the further understanding of AIDS and the development of AIDS prevention and a control scheme [11][12][13].…”