Numerical Analysis for a Fractional Differential Time-Delay Model of HIV Infection of CD4 +

We study a fractional differential model of HIV infection of CD4+ T-cell, in which the CD4+ T-cell proliferation plays an important role in HIV infection under antiretroviral therapy. An appropriate method is given to ensure that both the equilibria are asymptotically stable for τ≥0. We calculate the basic reproduction number R0, the IFE E0, two IPEs E1* and E2*, and so on, and judge the stability of the equilibrium. In addition, we describe the dynamic behaviors of the fractional HIV model by using the Adams-type predictor-corrector method algorithm. At last, we extend the model to incorporate the term which we consider the loss of virion and a bilinear term during attacking the target cells

Existence and Numerical Simulation of Solutions for Fractional Equations Involving Two Fractional Orders with Nonlocal Boundary Conditions

We study a boundary value problem for fractional equations involving two fractional orders. By means of a fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. In addition, we describe the dynamic behaviors of the fractional Langevin equation by using the G2 algorithm

Neuro-Adaptive Cooperative Tracking Rendezvous of Nonholonomic Mobile Robots

This brief proposes a neuro-adaptive method for the unsolved problem of cooperative tracking rendezvous of nonholonomic mobile robots (NMRs) subject to uncertain and unmodelled dynamics. A hierarchical cooperative control framework is proposed, which consists of a novel distributed estimator along with local neuro-adaptive tracking controllers. Rigorous stability analysis as well as simulation experiments illustrate the proposed method.</p

Recent Advances in the Aging Microenvironment of Breast Cancer

Aging is one of the risk factors for advanced breast cancer. With the increasing trend toward population aging, it is important to study the effects of aging on breast cancer in depth. Cellular senescence and changes in the aging microenvironment in vivo are the basis for body aging and death. In this review, we focus on the influence of the aging microenvironment on breast cancer. Increased breast extracellular matrix stiffness in the aging breast extracellular matrix can promote the invasion of breast cancer cells. The role of senescence-associated secretory phenotypes (SASPs) such as interleukin-6 (IL-6), IL-8, and matrix metalloproteases (MMPs), in breast cancer cell proliferation, invasion, and metastasis is worthy of exploration. Furthermore, the impact of senescent fibroblasts, adipocytes, and endothelial cells on the mammary matrix is discussed in detail. We also list potential targets for senotherapeutics and senescence-inducing agents in the aging microenvironment of breast cancer. In conclusion, this review offers an overview of the influence of the aging microenvironment on breast cancer initiation and progression, with the aim of providing some directions for future research on the aging microenvironment in breast cancer