Impact of delay on HIV-1 dynamics of fighting a virus with another virus

In this paper, we propose a mathematical model for HIV-1 infection with intracellular delay. The model examines a viral-therapy for controlling infections through recombining HIV-1 virus with a genetically modified virus. For this model, the basic reproduction number $\mathcal{R}_0$ are identified and its threshold properties are discussed. When $\mathcal{R}_0 < 1$, the infection-free equilibrium $E_0$ is globally asymptotically stable. When $\mathcal{R}_0 > 1$, $E_0$ becomes unstable and there occurs the single-infection equilibrium $E_s$, and $E_0$ and $E_s$ exchange their stability at the transcritical point $\mathcal{R}_0 =1$. If $1< \mathcal{R}_0 < R_1$, where $R_1$ is a positive constant explicitly depending on the model parameters, $E_s$ is globally asymptotically stable, while when $\mathcal{R}_0 > R_1$, $E_s$ loses its stability to the double-infection equilibrium $E_d$. There exist a constant $R_2$ such that $E_d$ is asymptotically stable if $R_1<\mathcal R_0 < R_2$, and $E_s$ and $E_d$ exchange their stability at the transcritical point $\mathcal{R}_0 =R_1$. We use one numerical example to determine the largest range of $\mathcal R_0$ for the local stability of $E_d$ and existence of Hopf bifurcation. Some simulations are performed to support the theoretical results. These results show that the delay plays an important role in determining the dynamic behaviour of the system. In the normal range of values, the delay may change the dynamic behaviour quantitatively, such as greatly reducing the amplitudes of oscillations, or even qualitatively changes the dynamical behaviour such as revoking oscillating solutions to equilibrium solutions. This suggests that the delay is a very important fact which should not be missed in HIV-1 modelling

Polarization screening and induced carrier density at the interface of LaAlO3_3 overlayer on SrTiO3_3 (001)

We investigate the role of lattice polarization in determination of induced carrier density at the $n$-type interface of LaAlO$_3$ overlayer on SrTiO$_3$ (001) by carrying out density-functional-theory calculations. When no oxygen vacancy or defect is present, the magnitude of polarization screening in the LaAlO$_3$ layers is found to be correlated with the carrier charge induced at the interface. For the interfaces with a few LaAlO$_3$ layers, the induced charge carrier is compensated by the electrostatic screening and consequently its density remains far less than 0.5 electrons per unit cell.Comment: 4 pages, 4 figure

Special Session on Industry 4.0

No abstract available

Parity violation in pre-inflationary bounce

The power suppression at largest scale in the CMB TT powerspectrum might imply the occurrence of a pre-inflationary bounce. We calculate the circularly polarized gravitational wave, leaded by the gravitational Chern-Simons term which universally appears in particle physics and string theory, in an inflationary background with the pre-inflationary bounce. The circularly polarized gravitational wave will induce TB and EB correlations at CMB last scatting surface. We find that although the BB powerspectrum at largest scale is also suppressed, the TB and EB powerspectra at corresponding scales may be enhanced.Comment: 15 pages, 4 figures,the final versio