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HIV infection is one of the most serious causes of death throughout the world. CD4+ T cells which play an important role in immune protection, are the primary targets for HIV infection. The hallmark of HIV infection is the progressive loss in population of CD4+ T cells. However, the pathway causing this slow T cell decline is poorly understood [16]. This paper studies a discontinuous mathematical model for HIV-1 infection, to investigate the effect of pyroptosis on the disease. For this purpose, we use the theory of discontinuous dynamical systems. In this way, we can better analyze the dynamical behavior of the HIV-1 system. Especially, considering the dynamics of the system on its discontinuity boundary enables us to obtain more comprehensive results rather than the previous researches. A stability region for the system, corresponding to its equilibria on the discontinuity boundary, will be determined. In such a parametric region, the trajectories of the system will be trapped on the discontinuity manifold forever. It is also shown that in the obtained stability region, the disease can lead to a steady state in which the population of uninfected T cells and viruses will preserve at a constant level of cytokines. This means that the pyroptosis will be restricted and the disease cannot progress for a long time. Some numerical simulations based on clinical and experimental data are given which are in good agreement with our theoretical results. [ABSTRACT FROM AUTHOR]

Nickel is one of the heavy metals, which is discharged to ecosystem by normal process and human actions. Nickel is regarded as crucial ion in the living creature and is a component of protein structure at very low level. Dispersive micro-solid-phase extraction assisted by ultrasonic waves with a new magnetic material using pyridine-functionalized magnetic nanoporous sorbent was utilized for detection of nickel ions at trace levels in real matrices. Magnetized nanoporous silica (MCM-41) was modified with pyridine groups, and the structure of prepared magnetic nanoporous sorbent was confirmed by instrumental techniques. The applied techniques were Fourier-transformed infrared spectroscopy, X-ray powder diffraction, transmission electron microscopy and thermogravimetry–differential thermal analysis. Preconcentrated nickel using the mentioned sample preparation procedure was monitored by GFAAS at ng L−1 concentrations. To optimize the effect of significant parameters on sorption and desorption of nickel ions using the applied sample preparation procedure, Box–Behnken design was utilized. The influencing parameters in the sorption step are: sorption amount (mg), pH of solution and sonication time (min), and these parameters for desorption step are: volume of eluent (mL), concentration of eluent (mol L−1) and sonication time (min). Optimized data for parameters that obtained by Box–Behnken design were: sample's pH: 7.5, sonication time for sorption: 8 min, sorbent amount: 24 mg, desorption solvent: HCl 1.2 mol L−1, eluent volume: 420 μL and time of sonication for desorption, 8 min. Relative standard deviation and method detection limit for nickel monitoring under optimized conditions by UA-d-μSPE were observed to be < 6% and 0.008 μg L−1, respectively. [ABSTRACT FROM AUTHOR]