Separable mixing: The general formulation and a particular example focusing on mask efficiency.

The aim of this short note is twofold. First, we formulate the general Kermack-McKendrick epidemic model incorporating static heterogeneity and show how it simplifies to a scalar Renewal Equation (RE) when separable mixing is assumed. A key general feature is that all information about the heterogeneity is encoded in one nonlinear real valued function of a real variable. Next, we specialize the model ingredients so that we can study the efficiency of mask wearing as a non-pharmaceutical intervention to reduce the spread of an infectious disease. Our main result affirms that the best way to protect the population as a whole is to protect yourself. This qualitative insight was recently derived in the context of an SIR network model. Here, we extend the conclusion to proportionate mixing models incorporating a general function describing expected infectiousness as a function of time since infection.

Quantifying within-household transmission of extended-spectrum ß-lactamase-producing bacteria.

OBJECTIVES: Patients can acquire extended-spectrum ß-lactamase (ESBL)-producing Enterobacteriaceae during hospitalization, and colonized patients may transmit these bacteria after discharge, most likely to household contacts. In this study, ESBL transmission was quantified in households. METHODS: Faecal samples were longitudinally collected from hospitalized patients colonized with ESBL-producing bacteria and from their household members during hospitalization of the index patient and at 3, 6, 12 and 18 months. A mathematical household model was developed, which allowed for person-to-person transmission, acquisition from other sources (background transmission), and losing carriage. Next, a deterministic population model with a household structure was created, informed by parameter values found in the household model. RESULTS: In all, 74 index patients and 84 household members were included. In more than half of the household members ESBL-producing bacteria were demonstrated at some time during follow up. Person-to-person transmission occurred at a rate of 0.0053/colonized person/day (0.0025-0.011), background transmission at 0.00015/day (95% CI 0.00002-0.00039), and decolonization at 0.0026/day (0.0016-0.0040) for index patients and 0.0090/day (0.0046-0.018) for household members. The estimated probability of transmission from an index patient to a household contact was 67% and 37% vice versa. CONCLUSION: There is frequent transmission of ESBL-producing bacteria in households, which may contribute to the observed endemicity of ESBL carriage in the Netherlands. However, the population model suggests that there is not a single dominant acquisition route in the community.

Epidemic potential of Escherichia coli ST131 and Klebsiella pneumoniae ST258: a systematic review and meta-analysis.

OBJECTIVES: Observational studies have suggested that Escherichia coli sequence type (ST) 131 and Klebsiella pneumoniae ST258 have hyperendemic properties. This would be obvious from continuously high incidence and/or prevalence of carriage or infection with these bacteria in specific patient populations. Hyperendemicity could result from increased transmissibility, longer duration of infectiousness, and/or higher pathogenic potential as compared with other lineages of the same species. The aim of our research is to quantitatively estimate these critical parameters for E. coli ST131 and K. pneumoniae ST258, in order to investigate whether E. coli ST131 and K. pneumoniae ST258 are truly hyperendemic clones. PRIMARY OUTCOME MEASURES: A systematic literature search was performed to assess the evidence of transmissibility, duration of infectiousness, and pathogenicity for E. coli ST131 and K. pneumoniae ST258. Meta-regression was performed to quantify these characteristics. RESULTS: The systematic literature search yielded 639 articles, of which 19 data sources provided information on transmissibility (E. coli ST131 n=9; K. pneumoniae ST258 n=10)), 2 on duration of infectiousness (E. coli ST131 n=2), and 324 on pathogenicity (E. coli ST131 n=285; K. pneumoniae ST258 n=39). Available data on duration of carriage and on transmissibility were insufficient for quantitative assessment. In multivariable meta-regression E. coli isolates causing infection were associated with ST131, compared to isolates only causing colonisation, suggesting that E. coli ST131 can be considered more pathogenic than non-ST131 isolates. Date of isolation, location and resistance mechanism also influenced the prevalence of ST131. E. coli ST131 was 3.2 (95% CI 2.0 to 5.0) times more pathogenic than non-ST131. For K. pneumoniae ST258 there were not enough data for meta-regression assessing the influence of colonisation versus infection on ST258 prevalence. CONCLUSIONS: With the currently available data, it cannot be confirmed nor rejected, that E. coli ST131 or K. pneumoniae ST258 are hyperendemic clones.

The effects of clinical and statistical heterogeneity on the predictive values of results from meta-analyses.

Variance between studies in a meta-analysis will exist. This heterogeneity may be of clinical, methodological or statistical origin. The last of these is quantified by the I(2) -statistic. We investigated, using simulated studies, the accuracy of I(2) in the assessment of heterogeneity and the effects of heterogeneity on the predictive value of meta-analyses. The relevance of quantifying I(2) was determined according to the likely presence of heterogeneity between studies (low, high, or unknown) and the calculated I(2) (low or high). The findings were illustrated by published meta-analyses of selective digestive decontamination and weaning protocols. As expected, I(2) increases and the likelihood of drawing correct inferences from a meta-analysis decreases with increasing heterogeneity. With low levels of heterogeneity, I(2) does not appear to be predictive of the accuracy of the meta-analysis result. With high levels of heterogeneity, even meta-analyses with low I(2) -values have low predictive values. Most commonly, the level of heterogeneity in a meta-analysis will be unknown. In these scenarios, I(2) determination may help to identify estimates with low predictive values (high I(2) ). In this situation, the results of a meta-analysis will be unreliable. With low I(2) -values and unknown levels of heterogeneity, predictive values of pooled estimates may range extensively, and findings should be interpreted with caution. In conclusion, quantifying statistical heterogeneity through I(2) -statistics is only helpful when the amount of clinical heterogeneity is unknown and I(2) is high. Objective methods to quantify the levels of clinical and methodological heterogeneity are urgently needed to allow reliable determination of the accuracy of meta-analyses.

Modeling non-inherited antibiotic resistance.

A mathematical model is presented for the increase and decrease of non-inherited antibiotic resistance levels in bacteria. The model is applied to experimental data on E. coli exposed to amoxicillin or tetracyclin in different concentrations. The parameters of the model are estimated using a Monte Carlo Markov Chain method. The model accurately describes build-up and decline of antibiotic resistance caused by physiological adaptations as long as no genetic changes have occurred. The main conclusion of the analysis is that short time periods are sufficient to re-obtain low MIC-values after long-lasting exposure to these antibiotics.

Transmissibility of livestock-associated methicillin-resistant Staphylococcus aureus (ST398) in Dutch hospitals.

We quantified nosocomial transmission rates of sequence type (ST) 398 methicillin-resistant Staphylococcus aureus (MRSA) (an emerging livestock-associated MRSA clone) and non-ST398 MRSA isolates in patients hospitalized without infection control measures in 51 Dutch hospitals. Identification of 174 index patients initiated 139 post-exposure screenings of 9925 persons. There were 65 genotype-confirmed secondary cases (three and 62 for ST398 and non-ST398 MRSA, respectively), yielding a relative transmission risk for ST398 MRSA of 0.28 (95% CI 0.09-0.90), which was not sensitive to adjustment for duration of hospitalization at time of detection. Nosocomial transmission of ST398 MRSA is 72% less likely than that of non-ST398 MRSA strains.

An algorithm to estimate the importance of bacterial acquisition routes in hospital settings.

An algorithm is presented to calculate likelihoods of acquisition routes using only individual patient data concerning period of stay and microbiologic surveillance (without genotyping). The algorithm also produces estimates for the prevalence and the number of acquisitions by each route. The algorithm is applied to colonization data of third-generation cephalosporin-resistant Enterobacteriaceae (CRE) from September 2001 to May 2002 in two intensive care units (ICUs) (n = 277 and n = 180, respectively) of Utrecht, Kingdom of the Netherlands. Genotyping and epidemiologic linkage are used as the reference standard. Surveillance cultures were obtained on admission and twice weekly thereafter. All CREs were genotyped. According to the reference standard, the daily prevalence of CRE in ICU-1 and ICU-2 was 26.1% (standard deviation: 15.4) and 15.1% (standard deviation: 13.4), respectively, with five of 23 (21.7%) and six of 21 (28.6%) cases of acquired colonization being of exogenous origin, respectively. On the basis of the algorithm, the endogenous route was responsible for more acquisitions than the exogenous route (p = 0.003 and p < 0.001 for ICU-1 and ICU-2, respectively). The estimated number of acquisitions is 30 and 27, and the estimated prevalence is 27.6% and 17.6% for ICU-1 and ICU-2, respectively. By use of longitudinal colonization data only, the algorithm determines the relative importance of acquisition routes taking patient dependency into account.

Controlling methicillin-resistant Staphylococcus aureus: quantifying the effects of interventions and rapid diagnostic testing.

Control of nosocomial transmission of methicillin-resistant Staphylococcus aureus (MRSA) has been unsuccessful in most countries. Yet, some countries have maintained low endemic levels by implementing nationwide MRSA-specific infection control measures, such as "search & destroy" (S&D). These strategies, however, are not based on well designed studies, and their use in countries with high levels of endemicity is controversial. We present a stochastic three-hospital model and an analytical one-hospital model to quantify the effectiveness of different infection control measures and to predict the effects of rapid diagnostic testing (RDT) on isolation needs. Isolation of MRSA carriers identified by clinical cultures is insufficient to control MRSA. However, combined with proactive search (of high-risk patients on admission and/or contacts of index patients), it will maintain prevalence levels <1%. Concerted implementation of S&D in countries with high nosocomial endemicity reduces nosocomial prevalence to <1% within 6 years. Stepwise implementation of control measures can reduce isolation capacities needed. RDT can reduce isolation needs by >90% in low-endemic settings and by 20% in high-endemic settings. Surveillance of colonization and improved hand hygiene can markedly increase control efficacy. These findings strongly suggest that: (i) causality exists between S&D and low MRSA prevalence; (ii) isolating MRSA carriers identified by clinical cultures as a single measure is insufficient for control; (iii) a combined approach of isolation and screening confers efficacy; and (iv) MRSA-prevalence levels can be reduced to <1% in high-endemic settings by S&D or a stepwise approach to interventions. RDT can markedly enhance feasibility.