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The time fractional-order nonlinear model of HIV-1 infection of T-cells with and without the rate of virus-producing cells’ death is very important in mathematical modeling. This paper presents proofs of the existence and uniqueness theorems using the Banach fixed point theorem, along with new approximate analytical solutions to two nonlinear fractional Equationuations characterizing HIV-1 infection in $CD{4^ + }$CD4+ T-cells. We use a combination of two methods, namely the natural transform method to deal with the linear terms and the Adomian decomposition method to deal with the nonlinear terms. There are two nonlinear numerical examples presented in this work, namely, we find approximate solutions to the time fractional-order nonlinear model of HIV-1 infection of T cells with and without the rate of virus-producing cells’ death using an effective method called the Adomian natural decomposition method (ANDM). The present approach, which has numerous applications in the science and engineering fields, is a great alternative to the many existing methods for solving systems of differential Equationuations. It also holds great promise for additional real-world applications. The Mathematica 12 package is used to carry out some of the nonlinear term calculations and the graphs presented in this work. [ABSTRACT FROM AUTHOR]

HIV-associated neurocognitive disorders (HAND) persist under antiretroviral therapy as a complex pathology that has been difficult to study in cellular and animal models. Therefore, we generated an ex vivo human brain slice model of HIV-1 infection from surgically resected adult brain tissue. Brain slice cultures processed for flow cytometry showed >90% viability of dissociated cells within the first three weeks in vitro, with parallel detection of astrocyte, myeloid, and neuronal populations. Neurons within brain slices showed stable dendritic spine density and mature spine morphologies in the first weeks in culture, and they generated detectable activity in multi-electrode arrays. We infected cultured brain slices using patient-matched CD4+ T-cells or monocyte-derived macrophages (MDMs) that were exposed to a GFP-expressing R5-tropic HIV-1 in vitro. Infected slice cultures expressed viral RNA and developed a spreading infection up to 9 days post-infection, which were significantly decreased by antiretrovirals. We also detected infected myeloid cells and astrocytes within slices and observed minimal effect on cellular viability over time. Overall, this human-centered model offers a promising resource to study the cellular mechanisms contributing to HAND (including antiretroviral toxicity, substance use, and aging), infection of resident brain cells, and new neuroprotective therapeutics. [ABSTRACT FROM AUTHOR]