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In this paper, the dynamical behaviors of a multiple delayed HIV-1 infection model which describes the interactions of humoral, cytotoxic T lymphocyte (CTL) immune responses, and two modes of transmission that are the classical virus-to-cell infection and the direct cell-to-cell transmission are investigated. The model incorporates three delays, including the delays of cell infection, virus production and activation of immune response. We first prove the well-posedness of the model, and calculate the biological existence of equilibria and the reproduction numbers, which contain virus infection, humoral immune response, CTL immune response, CTL immune competition, and humoral immune competition. Further, the threshold conditions for the local and global stability of the equilibria for infection-free, immune-free, antibody response, CTL response, and interior are established by utilizing linearization method and the Lyapunov functionals. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is investigated by using the bifurcation theory. Numerical simulations are carried out to illustrate the theoretical results and reveal the effects of some key parameters on viral dynamics. [ABSTRACT FROM AUTHOR]

In recent decades, AIDS has been one of the main challenges facing the medical community around the world. Due to the large human deaths of this disease, researchers have tried to study the dynamic behaviors of the infectious factor of this disease in the form of mathematical models in addition to clinical trials. In this paper, we study a new mathematical model in which the dynamics of CD 4 + T-cells under the effect of HIV-1 infection are investigated in the context of a generalized fractal-fractional structure for the first time. The kernel of these new fractal-fractional operators is of the generalized Mittag-Leffler type. From an analytical point of view, we first derive some results on the existence theory and then the uniqueness criterion. After that, the stability of the given fractal-fractional system is reviewed under four different cases. Next, from a numerical point of view, we obtain two numerical algorithms for approximating the solutions of the system via the Adams-Bashforth method and Newton polynomials method. We simulate our results via these two algorithms and compare both of them. The numerical results reveal some stability and a situation of lacking a visible order in the early days of the disease dynamics when one uses the Newton polynomial. [ABSTRACT FROM AUTHOR]

Introduction: The purpose of the study was to assess hepcidin levels and iron metabolism in otherwise healthy human immunodeficiency virus-1 (HIV-1)-infected males and the influence of antiretroviral therapy on hepcidin production, as data in this group are scarce. Methods: A total of 89 HIV-1-infected males, 42 on effective antiretroviral therapy (ART)—group A, 47 treatment-naïve—group B, and 27 healthy controls—group C, were enrolled. Erythrocytes parameters, iron metabolism parameters, hepcidin, highly sensitive C-reactive protein (hsCRP), interleukin 6 (IL-6), and soluble transferrin receptor (sTfR) levels were assessed. Conditions related to inflammatory activity, systemic metabolic diseases and iron supplementation were exclusion criteria. Convenience sampling was used. Results: Median age in HIV-1 group was 33 years, and 27 years in the control group. Median CD4+ T-cell count was 724 cells/μl in group A, and 488 cells/μl in group B (p = 0.0000). Nadir CD4+ T-cell count was 397 cells/μl in group A and 475 cells/μl in group B (p = 0.0001). Median value of HIV-1 viral load (VL) in group B was 16 900 copies/mL. The hepcidin value was lower in group A than in groups B (p = 0.0008) or C (p = 0.0004), without differences between groups B and C. The hepcidin value correlated with ferritin in groups A (r2 = 0.16; p = 0.008) and B (r2 = 0.39; p = 0.000), but not in group C (r2 = 0.11; p = 0.09). In group A, the hepcidin value correlated with current CD4+ count (r = 0.48, p = 0.0012), but there was no correlation in group B. There were no correlations of hepcidin values with CD4+ T cell nadir in group A (p = 0.371) or in group B (p = 0.477); ART period (p = 0.614); VL in group B (p = 0.71). No abnormalities of iron metabolism, hsCRP, IL-6, or sTfR were noted. Conclusions: Asymptomatic HIV-1 infection does not cause clinically important iron metabolism alterations or increased hepcidin production. Hepcidin values decrease on effective antiretroviral therapy. [ABSTRACT FROM AUTHOR]