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This paper discusses a randomized non-autonomous logistic equationstandard Brownian motion. In [D.Q. Jiang, N.Z. Shi, A note on non-autonomous logistic equation with random perturbation, J. Math. Anal. Appl. 303 (2005) 164-172], the authors show that E[1/N (t)] has a unique positive T -periodic solution E[1/N p (t)] provided a(t), b(t) and α(t) are continuous T -periodic functions, a(t) > 0, b(t) > 0 and T 0 [a(s) − α 2 (s)] ds > 0. We show that this equation is stochastically permanent and the solution N p (t) is globally attractive provided a(t), b(t) and α(t) are continuous T -periodic functions, a(t) > 0, b(t) > 0 and min t∈[0,T ] a(t) > max t∈[0,T ] α 2 (t). By the way, the similar results of a generalized non-autonomous logistic equation with random perturbation are yielded.

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This paper discusses a randomized nonautonomous logistic equationwhere B(t) is 1-dimensional standard Brownian motion. We show that E[1/N(t)] has a unique positive T -periodic solution E[1/N p (t)] provided a(t), b(t), and α(t) are continuous T -periodic functions, a(t) > 0, b(t) > 0 and T 0 [a(s) − α 2 (s)] ds > 0.  2004 Elsevier Inc. All rights reserved.

Chimeric antigen receptor (CAR) modified T cells targeted CD19 showed promising clinical outcomes in treatment of B cell malignances such as chronic lymphocytic leukemia (CLL), acute lymphoblastic leukemia (ALL) and other indolent lymphomas. However, the clinical benefit varies tremendously among different trials. This meta-analysis investigated the efficacy (response rates and survival time) of CD19-CAR T cells in refractory B cell malignances in Phase I clinical trials. We searched publications between 1991 and 2014 from PubMed and Web of Science. Pooled response rates were calculated using random-effects models. Heterogeneity was investigated by subgroup analysis and meta-regression. Fourteen clinical trials including 119 patients were eligible for response rate evaluation, 62 patients in 12 clinical trials were eligible for progression-free survival analysis. The overall pooled response rate of CD19-CAR T cells was 73% (95% confidence interval [CI]: 46-94%). Significant heterogeneity across estimates of response rates was observed (p < 0.001, I2=88.3%). ALL patients have higher response rate (93%, 95% CI: 65-100%) than CLL (62%, 95% CI: 27-93%) and lymphoma patients (36%, 95% CI: 1-83%). Meta-regression analysis identified lymphodepletion and no IL-2 administrated T cells as two key factors associated with better clinical response. Lymphodepletion and higher infused CAR T cell number were associated with better prognosis. In conclusion, this meta-analysis showed a high clinical response rate of CD19-CAR T cell-based immunotherapy in treatment of refractory B cell malignancies. Lymphodepletion and increasing number of infused CD19-CAR T cells have positive correlations with the clinical efficiency, on the contrary, IL-2 administration to T cells is not recommended.

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