A nonstandard finite difference scheme and optimal control for an HIV model with Beddington-DeAngelis incidence and cure rate
EUROPEAN PHYSICAL JOURNAL PLUS
Authors: Salman, Sanaa Moussa
Abstract
In this paper, we incorporate the Beddington-DeAngelis incidence rate to a continuous-time HIV infection model with cure rate and a full logistic proliferation rate of CD4(+) T cells in both uninfected and infected cells. Equilibria and their local stability analysis are discussed. It is shown that the HIV-free equilibrium point is locally asymptotically stable if R-0 < 1 and unstable if R-0 >= 1, where R-0 is the basic reproduction number. Whereas, the HIV equilibrium point is locally asymptotically stable if R-0 > 1. Anonstandard finite difference method is applied to the continuous model to obtain its discrete counterpart. The scheme applied preserves the main features of the continuous model such as positivity, boundedness of the solutions, equilibria and their local stability. Moreover, an optimal control strategy is applied to the discrete-time model in order to reduce the number of infected cells as well as the number of free HIV particles. Numerical simulations are performed to verify the theoretical analysis obtained.
Patterns of immune infi ltration in stable and raptured abdominal aortic aneurysms: A gene-expression-based retrospective study
GENE
Authors: Lei, Chuxiang; Yang, Dan; Chen, Siliang; Chen, Wenlin; Sun, Xiaoning; Wu, Xiao; Chen, Mengyin; Li, Yuan; Zheng, Yuehong
Abstract
Background: Abdominal aortic aneurysm (AAA) is a disease characterized by weakening arterial wall and per-manent expansion with high mortality once rupture, which was involved with immune system activation. However, owing to technical difficulties, previous research has limited the impact of one or limited immune cells on AAA. Methods: We analyzed the composition of immune cells using the CIBERSORT algorithm through transcriptome sequencing data from patients with stable (eAAA) and ruptured aneurysms (rAAA). The whole transcriptome sequencing data, including 17 patients with ruptured AAA and 31 patients with stable AAA were downloaded from Gene Expression Omnibus (GEO, GSE98278). After normalizing and data processing, five rAAA and seventeen eAAA patients entered the follow-up analysis. We performed Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) analysis to identify several pathways that were significantly enriched in rAAA compared to eAAA tissues. Results: We demonstrated that the compositions of infiltrative immune cell in eAAA and rAAA were different. Naive B cells, both resting and activated CD4+ memory T cells were found significantly higher in ruptured AAA, while memory B cells and activated mast cells were much less in ruptured AAA than that in stable AAA. Besides, PTX3 was significantly highly expressed in rAAA, which might be associated with the complement system and polarization of macrophages. Finally, differentially expressed genes and the related immune cells were mapped in a network to reveal the relationship between gene expression and infiltrative immune cells. Conclusion: We identified the infiltrated immune cell profile of eAAA and rAAA patients, which might be the potential target of AAA treatment.