Almost sure convergence of maxima for chaotic dynamical systems

ArticleSuppose (f,X,ν) is a measure preserving dynamical system and ϕ:X→R is an observable with some degree of regularity. We investigate the maximum process M n :=max{X 1 ,…,X n } , where X i =ϕ∘f i is a time series of observations on the system. When M n →∞ almost surely, we establish results on the almost sure growth rate, namely the existence (or otherwise) of a sequence u n →∞ such that M n /u n →1 almost surely. The observables we consider will be functions of the distance to a distinguished point x ~ ∈X . Our results are based on the interplay between shrinking target problem estimates at x ~ and the form of the observable (in particular polynomial or logarithmic) near x ~ . We determine where such an almost sure limit exists and give examples where it does not. Our results apply to a wide class of non-uniformly hyperbolic dynamical systems, under mild assumptions on the rate of mixing, and on regularity of the invariant measure

Incidence and severity of childhood pneumonia in the first year of life in a South African birth cohort: the Drakenstein Child Health Study

Background Childhood pneumonia causes substantial mortality and morbidity. Accurate measurements of pneumonia incidence are scarce in low-income and middle-income countries, particularly after implementation of pneumococcal conjugate vaccine. We aimed to assess the incidence, severity, and risk factors for pneumonia in the fi rst year of life in children enrolled in a South African birth cohort. Methods This birth cohort study is being done at two sites in Paarl, a periurban area of South Africa. We enrolled pregnant women (>18 years) and followed up mother–infant pairs to 1 year of age. We obtained data for risk factors and respiratory symptoms. Children received 13-valent pneumococcal conjugate vaccine according to national immunisation schedules. We established pneumonia surveillance systems and documented episodes of ambulatory pneumonia and pneumonia warranting hospital admission. We calculated incidence rate ratios for pneumonia with mixed-eff ects Poisson regression. Findings Between May 29, 2012 and May 31, 2014, we enrolled 697 infants who accrued 513 child-years of follow-up. We recorded 141 pneumonia episodes, with an incidence of 0·27 episodes per child-year (95% CI 0·23–0·32). 32 (23%) pneumonia cases were severe pneumonia, with an incidence of 0·06 episodes per child-year (95% CI 0·04–0·08). Two (1%) of 141 pneumonia episodes led to death from pneumonia. Maternal HIV, maternal smoking, male sex, and malnutrition were associated with an increased incidence of pneumonia. Interpretation Pneumonia incidence was high in the fi rst year of life, despite a strong immunisation programme including 13-valent pneumococcal conjugate vaccine. Incidence was associated with pneumonia risk factors that are amenable to interventions. Prevention of childhood pneumonia through public health interventions to address these risk factors should be strengthened. Funding Bill & Melinda Gates Foundation, South African Thoracic Society, Federation of Infectious Diseases Societies of South Africa, and University of Cape Town

Comparison of a real-time multiplex PCR and sequetyping assay for pneumococcal serotyping

BACKGROUND: Pneumococcal serotype identification is essential to monitor pneumococcal vaccine effectiveness and serotype replacement. Serotyping by conventional serological methods are costly, labour-intensive, and require significant technical expertise. We compared two different molecular methods to serotype pneumococci isolated from the nasopharynx of South African infants participating in a birth cohort study, the Drakenstein Child Health Study, in an area with high 13-valent pneumococcal conjugate vaccine (PCV13) coverage. METHODS: A real-time multiplex PCR (rmPCR) assay detecting 21 different serotypes/-groups and a sequetyping assay, based on the sequence of the wzh gene within the pneumococcal capsular locus, were compared. Forty pneumococcal control isolates, with serotypes determined by the Quellung reaction, were tested. In addition, 135 pneumococcal isolates obtained from the nasopharynx of healthy children were tested by both serotyping assays and confirmed by Quellung testing. Discordant results were further investigated by whole genome sequencing of four isolates. RESULTS: Of the 40 control isolates tested, 25 had a serotype covered by the rmPCR assay. These were all correctly serotyped/-grouped. Sequetyping PCR failed in 7/40 (18%) isolates. For the remaining isolates, sequetyping assigned the correct serotype/-group to 29/33 (88%) control isolates. Of the 132/135 (98%) nasopharyngeal pneumococcal isolates that could be typed, 69/132 (52%) and 112/132 (85%) were assigned the correct serotype/-group by rmPCR and sequetyping respectively. The serotypes of 63/132 (48%) isolates were not included in the rmPCR panel. All except three isolates (serotype 25A and 38) were theoretically amplified and differentiated into the correct serotype/-group with some strains giving ambigous results (serotype 13/20, 17F/33C, and 11A/D/1818F). Of the pneumococcal serotypes detected in this study, 69/91 (76%) were not included in the current PCV13. The most frequently identified serotypes were 11A, 13, 15B/15C, 16F and 10A. CONCLUSION: The rmPCR assay performed well for the 21 serotypes/-groups included in the assay. However, in our study setting, a large proportion of serotypes were not detected by rmPCR. The sequetyping assay performed well, but did misassign specific serotypes. It may be useful for regions where vaccine serotypes are less common, however confirmatory testing is advisable

Longitudinal Population Dynamics of Staphylococcus aureus in the Nasopharynx During the First Year of Life

Background:Staphylococcus aureus colonization is a risk factor for invasive disease. Few studies have used strain genotype data to study S. aureus acquisition and carriage patterns. We investigated S. aureus nasopharyngeal carriage in infants in an intensively sampled South African birth cohort.Methods: Nasopharyngeal swabs were collected at birth and fortnightly from 137 infants through their first year of life. S. aureus was characterized by spa-typing. The incidence of S. aureus acquisition, and median carriage duration for each genotype was determined. S. aureus carriage patterns were defined by combining the carrier index (proportion of samples testing positive for S. aureus) with genotype diversity measures. Persistent or prolonged carriage were defined by a carrier index ≥0.8 or ≥0.5, respectively. Risk factors for time to acquisition of S. aureus were determined.Results: Eighty eight percent (121/137) of infants acquired S. aureus at least once. The incidence of acquisition at the species and genotype level was 1.83 and 2.8 episodes per child-year, respectively. No children had persistent carriage (defined as carrier index of >0.8). At the species level 6% had prolonged carriage, while only 2% had prolonged carriage with the same genotype. Carrier index correlated with the absolute number of spa-CCs carried by each infant (r = 0.5; 95% CI 0.35–0.62). Time to first acquisition of S. aureus was shorter in children from households with ≥5 individuals (HR 1.06, 95% CI 1.07–1.43), with S. aureus carrier mothers (HR; 1.5, 95% CI 1.2–2.47), or with a positive tuberculin skin test during the first year of life (HR; 1.81, 95% CI 0.97–3.3).Conclusion: Using measures of genotype diversity, we showed that S. aureus NP carriage is highly dynamic in infants. Prolonged carriage with a single strain occurred rarely; persistent carriage was not observed. A correlation was observed between carrier index and genotype diversity

Modern lineages of Mycobacterium tuberculosis exhibit lineage-specific patterns of growth and cytokine induction in human monocyte-derived macrophages

BACKGROUND: Strains of Mycobacterium tuberculosis vary in virulence. Strains that have caused outbreaks in the United States and United Kingdom have been shown to subvert the innate immune response as a potential immune evasion mechanism. There is, however, little information available as to whether these patterns of immune subversion are features of individual strains or characteristic of broad clonal lineages of M. tuberculosis . METHODS: Strains from two major modern lineages (lineage 2 [East-Asian] and lineage 4 [Euro-American]) circulating in the Western Cape in South Africa as well as a comparator modern lineage (lineage 3 [CAS/Delhi]) were identified. We assessed two virulence associated characteristics: mycobacterial growth (in liquid broth and monocyte derived macrophages) and early pro-inflammatory cytokine induction. RESULTS: In liquid culture, Lineage 4 strains grew more rapidly and reached higher plateau levels than other strains (lineage 4 vs. lineage 2 p = 0.0024; lineage 4 vs. lineage 3 p = 0.0005). Lineage 3 strains were characterized by low and early plateau levels, while lineage 2 strains showed an intermediate growth phenotype. In monocyte-derived macrophages, lineage 2 strains grew faster than lineage 3 strains (p<0.01) with lineage 4 strains having an intermediate phenotype. Lineage 2 strains induced the lowest levels of pro-inflammatory TNF and IL-12p40 as compared to other lineages (lineage 2: median TNF 362 pg/ml, IL-12p40 91 pg/ml; lineage 3: median TNF 1818 pg/ml, IL-12p40 123 pg/ml; lineage 4: median TNF 1207 pg/ml, IL-12p40 205 pg/ml;). In contrast, lineage 4 strains induced high levels of IL-12p40 and intermediate level of TNF. Lineage 3 strains induced high levels of TNF and intermediate levels of IL-12p40. CONCLUSIONS: Strains of M. tuberculosis from the three major modern strain lineages possess distinct patterns of growth and cytokine induction. Rapid growth and immune subversion may be key characteristics to the success of these strains in different human populations

Outbreak of multi-drug resistant Pseudomonas aeruginosa bloodstream infection in the haematology unit of a South African academic hospital

Objective: To describe an outbreak of multi-resistant Pseudomonas aeruginosa bloodstream infections (MRPA-BSI) that occurred in the haematology ward of a tertiary academic hospital in Cape Town, South Africa, and determine risk factors for acquisition of MRPA-BSI. METHODS: The outbreak investigation included a search for additional cases, review of patient records, environmental and staff screening, molecular typing using pulsed-field gel electrophoresis (PFGE) and Multi-locus sequencing (MLST) and a retrospective case-control study. RESULTS: Ten MRPA-BSI cases occurred in the haematology ward between January 2010 and January 2011. The case fatality rate was 80%. Staff screening specimens were negative for MRPA and an environmental source was not identified. PFGE showed that 9/10 isolates were related. MLST showed that 3 of these 9 isolates belonged to Sequence type (ST) 233 while the unrelated isolate belonged to ST260. CONCLUSION: We have described an outbreak of MRPA-BSI occurring over an extended period of time among neutropenic haematology patients. Molecular typing confirms that the outbreak was predominantly due to a single strain. The source of the outbreak was not identified, but the outbreak appears to have been controlled following intensive infection control measures

Development of a clinical prediction rule to diagnose Pneumocystis jirovecii pneumonia in the World Health Organization’s algorithm for seriously ill HIV-infected patients

Background: The World Health Organization (WHO) algorithm for the diagnosis of tuberculosis in seriously ill HIV-infected patients recommends that treatment for Pneumocystis jirovecii pneumonia (PJP) should be considered without giving clear guidance on selecting patients for empiric PJP therapy. PJP is a common cause of hospitalisation in HIV-infected patients in resource-poor settings where diagnostic facilities are limited.Methods: We developed clinical prediction rules for PJP in a prospective cohort of HIVinfected inpatients with WHO danger signs and cough of any duration. The reference standard for PJP was &gt; 1000 copies/mL of P. jirovecii DNA on real-time sputum polymerase chain reaction (PCR). Four potentially predictive variables were selected for regression models: dyspnoea, chest X-ray, haemoglobin and oxygen saturation. Respiratory rate was explored as a replacement for oxygen saturation as pulse oximetry is not always available in resource-poor settings.Results: We enrolled 500 participants. After imputation for missing values, there were 56 PJP outcome events. Dyspnoea was not independently associated with PJP. Oxygen saturation and respiratory rate were inversely correlated. Two clinical prediction rules were developed: chest X-ray possible/likely PJP, haemoglobin ≥ 9 g/dL and either oxygen saturation &lt; 94% or respiratory rate. The area under the receiver operating characteristic curve of the clinical prediction rule models was 0.761 (95% CI 0.683–0.840) for the respiratory rate model and 0.797 (95% CI 0.725–0.868) for the oxygen saturation model. Both models had zero probability for PJP for scores of zero, and positive likelihood ratios exceeded 10 for high scores.Conclusion: We developed simple clinical prediction rules for PJP, which, if externally validated, could assist decision-making in the WHO seriously ill algorithm