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A continuous-state branching process with immigration having branching mechanism
and immigration mechanism
, a CBI
process for short, may have either of two different asymptotic regimes, depending on whether
, the CBI process has either a limit distribution or a growth rate dictated by the branching dynamics. When
, immigration overwhelms branching dynamics. Asymptotics in the latter case are studied via a nonlinear time-dependent renormalization in law. Three regimes of weak convergence are exhibited. Processes with critical branching mechanisms subject to a regular variation assumption are studied. This article proves and extends results stated by M. Pinsky in ‘Limit theorems for continuous state branching processes with immigration’ (Bull. Amer. Math. Soc.78, 1972).
The Centers for Disease Control and Prevention (CDC) has developed an approach to ventilator-associated events (VAE) surveillance. Using these methods, this study was performed to investigate VAE incidences and to test whether VAEs are associated with poorer outcomes in China.
A 4-month, prospective multicenter surveillance study between April and July 2013.
Our study included 15 adult intensive care units (ICUs) of 15 hospitals in China.
Patients admitted to ICUs during the study period
Patients on mechanical ventilation (MV) were monitored for VAEs: ventilator-associated conditions (VACs), infection-related ventilator-associated complications (IVACs), and possible or probable ventilator-associated pneumonia (VAP). Patients with and without VACs were compared with regard to duration of MV, ICU length of stay (LOS), overall hospital LOS, and mortality rate.
During the study period, 2,356 of the 5,256 patients admitted to ICUs received MV for 8,438 ventilator days. Of these patients, 636 were on MV >2 days. VACs were identified in 94 cases (4.0%; 11.1 cases per 1,000 ventilator days), including 31 patients with IVACs and 16 with possible VAP but none with probable VAP. Compared with patients without VACs, patients with VACs had longer ICU LOS (by 6.2 days), longer duration on MV (by 7.7 days), and higher hospital mortality rate (50.0% vs 27.3%). The mortality rate attributable to VACs was 11.7%. Compared with those with VACs alone, patients with IVACs had longer duration on MV and increased ICU LOS but no higher mortality rates.
In China, surveillance of VACs and IVACs is able to identify MV patients with poorer outcomes. However, surveillance of possible and probable VAP can be problematic.
Infect. Control Hosp. Epidemiol. 2015;36(12):1388–1395
We consider a dynamic metapopulation involving one large population of size N surrounded by colonies of size εNN, usually called peripheral isolates in ecology, where N → ∞ and εN → 0 in such a way that εNN → ∞. The main population, as well as the colonies, independently send propagules to found new colonies (emigration), and each colony independently, eventually merges with the main population (fusion). Our aim is to study the genealogical history of a finite number of lineages sampled at stationarity in such a metapopulation. We make assumptions on model parameters ensuring that the total outer population has size of the order of N and that each colony has a lifetime of the same order. We prove that under these assumptions, the scaling limit of the genealogical process of a finite sample is a censored coalescent where each lineage can be in one of two states: an inner lineage (belonging to the main population) or an outer lineage (belonging to some peripheral isolate). Lineages change state at constant rate and (only) inner lineages coalesce at constant rate per pair. This two-state censored coalescent is also shown to converge weakly, as the landscape dynamics accelerate, to a time-changed Kingman coalescent.
The conditional least-squares estimators of the variances are studied for a critical branching process with immigration that allows the offspring distributions to have infinite fourth moments. We derive different forms of limiting distributions for these estimators when the offspring distributions have regularly varying tails with index α. In particular, in the case in which 2 < α < 8/3, the normalizing factor of the estimator for the offspring variance is smaller than √n, which is different from that of Winnicki (1991).
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