Stability of HIV-1 Dynamics Models with Viral and Cellular Infections in the Presence of Macrophages

Abstract

In this research work, we suggest two mathematical models that take into account (i) two categories of target cells, CD4+T cells and macrophages, and (ii) two modes of infection transmissions, the direct virus-to-cell (VTC) method and cell-to-cell (CTC) infection transmission, where CTC is an effective method of spreading human immunodeficiency virus type-1 (HIV-1), as with the VTC method. The second model incorporates four time delays. In both models, the presence of a bounded and positive solution of the biological model is investigated. The existence conditions of all equilibria are established. The basic reproduction number R0 that identifies a disease index is obtained. Lyapunov functions are utilized to verify the global stability of all equilibria. The theoretical findings are verified through numerical simulations. According to the outcomes, the trajectories of the solutions approach the infection-free equilibrium and infection-present equilibrium when R0≤1 and R0>1, respectively. Further, we study the sensitivity analysis to investigate how the values of all the parameters of the suggested model affect R0 for given data. We discuss the impact of the time delay on HIV-1 progression. We find that a longer time delay results in suppression of the HIV-1 infection and vice versa.

Keywords

• HIV-1 infection
• Lyapunov function
• global stability
• time delay
• sensitivity analysis