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

Divide and Fuse: A Re-ranking Approach for Person Re-identification

As re-ranking is a necessary procedure to boost person re-identification (re-ID) performance on large-scale datasets, the diversity of feature becomes crucial to person reID for its importance both on designing pedestrian descriptions and re-ranking based on feature fusion. However, in many circumstances, only one type of pedestrian feature is available. In this paper, we propose a "Divide and use" re-ranking framework for person re-ID. It exploits the diversity from different parts of a high-dimensional feature vector for fusion-based re-ranking, while no other features are accessible. Specifically, given an image, the extracted feature is divided into sub-features. Then the contextual information of each sub-feature is iteratively encoded into a new feature. Finally, the new features from the same image are fused into one vector for re-ranking. Experimental results on two person re-ID benchmarks demonstrate the effectiveness of the proposed framework. Especially, our method outperforms the state-of-the-art on the Market-1501 dataset.Comment: Accepted by BMVC201