Heat and Poisson semigroups for Fourier-Neumann expansions

Given $\alpha > -1$, consider the second order differential operator in $(0,\infty)$, $$L_\alpha f \equiv (x^2 \frac{d^2}{dx^2} + (2\alpha+3)x \frac{d}{dx} + x^2 + (\alpha+1)^2)(f),$$ which appears in the theory of Bessel functions. The purpose of this paper is to develop the corresponding harmonic analysis taking $L_\alpha$ as the analogue to the classical Laplacian. Namely we study the boundedness properties of the heat and Poisson semigroups. These boundedness properties allow us to obtain some convergence results that can be used to solve the Cauchy problem for the corresponding heat and Poisson equations.Comment: 16 page

Effectiveness of GenoType MTBDRsl in excluding TB drug resistance in a clinical trial

OBJECTIVES: To assess the performance of the GenoType MTBDRsl v1, a line-probe assay (LPA), to exclude baseline resistance to fluoroquinolones (FQs) and second-line injectables (SLIs) in the Standard Treatment Regimen of Anti-tuberculosis Drugs for Patients With MDR-TB 1 (STREAM 1) trial. METHODS: Direct sputum MTBDRsl results in the site laboratories were compared to indirect phenotypic drug susceptibility testing (pDST) results in the central laboratory, with DNA sequencing as a reference standard. RESULTS: Of 413 multidrug-resistant TB (MDR-TB) patients tested using MTBDRsl and pDST, 389 (94.2%) were FQ-susceptible and 7 (1.7%) FQ-resistant, while 17 (4.1%) had an inconclusive MTBDRsl result. For SLI, 372 (90.1%) were susceptible, 5 (1.2%) resistant and 36 (8.7%) inconclusive. There were 9 (2.3%) FQ discordant pDST/MTBDRsl results, of which 3 revealed a mutation and 5 (1.3%) SLI discordant pDST/MTBDRsl results, none of which were mutants on sequencing. Among the 17 FQ- and SLI MTBDRsl-inconclusive samples, sequencing showed 1 FQ- and zero SLI-resistant results, similar to frequencies among the conclusive MTBDRsl. The majority of inconclusive MTBDRsl results were associated with low bacillary load samples (acid-fast bacilli smear-negative or scantily positive) compared to conclusive results (P < 0.001). CONCLUSION: MTBDRsl can facilitate the rapid exclusion of FQ and SLI resistances for enrolment in clinical trials

Evaluation of spoligotyping in a study of the transmission of Mycobacterium tuberculosis

Spoligotyping (for spacer oligotyping) is an easy, economical, and rapid way of typing Mycobacterium tuberculosis complex strains with the DR spacer markers (J. Kamerbeek et al., J. Clin. Microbiol. 35:907-914, 1997; D. van Soolingen et al., 33:3234-3248, 1995). The stability of the markers was demonstrated by showing that all the Mycobacterium bovis BCG strains tested gave the same spoligotyping pattern. None of the 42 atypical mycobacterial strains tested gave a spoligotyping signal, indicating the specificity of the technique for M. tuberculosis complex. The utility of the spoligotyping method was demonstrated by analyzing 106 isolates of M. tuberculosis obtained over 1 year in three Paris hospitals. The results obtained by this technique were compared to those obtained by Torrea et al. (G. Torrea et al., J. Clin. Microbiol. 34:1043-1049, 1996) by IS6110-based restriction fragment length polymorphism (RFLP) analysis. Strains from patients with epidemiological relationships that were in the same IS6110-RFLP cluster were also in the same spoligotyping group. Spoligotyping was more discriminative than RFLP analysis for strains with one or two copies of IS6110. RFLP analysis did not discriminate between the nine strains with one or two IS6110 bands with no known epidemiological relation, whereas spoligotyping distinguished between eight different types. IS6I10-RFLP analysis split some of the spoligotyping clusters, particularly when the IS6110 copy number was high. Therefore, we propose a strategy for typing M. tuberculosis strains in which both markers are used.</jats:p

Multidrug-resistant tuberculosis control in Rwanda overcomes a successful clone that causes most disease over a quarter century

Summary background: Multidrug-resistant (MDR) tuberculosis (TB) poses an important challenge in TB management and control. Rifampicin resistance (RR) is a solid surrogate marker of MDR-TB. We investigated the RR-TB clustering rates, bacterial population dynamics to infer transmission dynamics, and the impact of changes to patient management on these dynamics over 27 years in Rwanda. Methods: We analysed whole genome sequences of a longitudinal collection of nationwide RR-TB isolates. The collection covered three important periods: before programmatic management of MDR-TB (PMDT; 1991–2005), the early PMDT phase (2006–2013), in which rifampicin drug-susceptibility testing (DST) was offered to retreatment patients only, and the consolidated phase (2014–2018), in which all bacteriologically confirmed TB patients had rifampicin DST done mostly via Xpert MTB/RIF assay. We constructed clusters based on a 5 SNP cut-off and resistance conferring SNPs. We used Bayesian modelling for dating and population size estimations, TransPhylo to estimate the number of secondary cases infected by each patient, and multivariable logistic regression to assess predictors of being infected by the dominant clone. Results: Of 308 baseline RR-TB isolates considered for transmission analysis, the clustering analysis grouped 259 (84.1%) isolates into 13 clusters. Within these clusters, a single dominant clone was discovered containing 213 isolates (82.2% of clustered and 69.1% of all RR-TB), which we named the “Rwanda Rifampicin-Resistant clone” (R3clone). R3clone isolates belonged to Ugandan sub-lineage 4.6.1.2 and its rifampicin and isoniazid resistance were conferred by the Ser450Leu mutation in rpoB and Ser315Thr in katG genes, respectively. All R3clone isolates had Pro481Thr, a putative compensatory mutation in the rpoC gene that likely restored its fitness. The R3clone was estimated to first arise in 1987 and its population size increased exponentially through the 1990s’, reaching maximum size (∼84%) in early 2000 s’, with a declining trend since 2014. Indeed, the highest proportion of R3clone (129/157; 82·2%, 95%CI: 75·3–87·8%) occurred between 2000 and 13, declining to 64·4% (95%CI: 55·1-73·0%) from 2014 onward. We showed that patients with R3clone detected after an unsuccessful category 2 treatment were more likely to generate secondary cases than patients with R3clone detected after an unsuccessful category 1 treatment regimen. Conclusions: RR-TB in Rwanda is largely transmitted. Xpert MTB/RIF assay as first diagnostic test avoids unnecessary rounds of rifampicin-based TB treatment, thus preventing ongoing transmission of the dominant R3clone. As PMDT was intensified and all TB patients accessed rifampicin-resistance testing, the nationwide R3clone burden declined. To our knowledge, our findings provide the first evidence supporting the impact of universal DST on the transmission of RR-TB

Effectiveness of GenoType MTBDRsl in excluding TB drug resistance in a clinical trial

OBJECTIVES: To assess the performance of the GenoType MTBDRsl v1, a line-probe assay (LPA), to exclude baseline resistance to fluoroquinolones (FQs) and second-line injectables (SLIs) in the Standard Treatment Regimen of Anti-tuberculosis Drugs for Patients With MDR-TB 1 (STREAM 1) trial. METHODS: Direct sputum MTBDRsl results in the site laboratories were compared to indirect phenotypic drug susceptibility testing (pDST) results in the central laboratory, with DNA sequencing as a reference standard. RESULTS: Of 413 multidrug-resistant TB (MDR-TB) patients tested using MTBDRsl and pDST, 389 (94.2%) were FQ-susceptible and 7 (1.7%) FQ-resistant, while 17 (4.1%) had an inconclusive MTBDRsl result. For SLI, 372 (90.1%) were susceptible, 5 (1.2%) resistant and 36 (8.7%) inconclusive. There were 9 (2.3%) FQ discordant pDST/MTBDRsl results, of which 3 revealed a mutation and 5 (1.3%) SLI discordant pDST/MTBDRsl results, none of which were mutants on sequencing. Among the 17 FQ- and SLI MTBDRsl-inconclusive samples, sequencing showed 1 FQ- and zero SLI-resistant results, similar to frequencies among the conclusive MTBDRsl. The majority of inconclusive MTBDRsl results were associated with low bacillary load samples (acid-fast bacilli smear-negative or scantily positive) compared to conclusive results (P < 0.001). CONCLUSION: MTBDRsl can facilitate the rapid exclusion of FQ and SLI resistances for enrolment in clinical trials

Effectiveness of GenoType MTBDR<i>sl</i> in excluding TB drug resistance in a clinical trial

OBJECTIVES: To assess the performance of the GenoType MTBDRsl v1, a line-probe assay (LPA), to exclude baseline resistance to fluoroquinolones (FQs) and second-line injectables (SLIs) in the Standard Treatment Regimen of Anti-tuberculosis Drugs for Patients With MDR-TB 1 (STREAM 1) trial.METHODS: Direct sputum MTBDRsl results in the site laboratories were compared to indirect phenotypic drug susceptibility testing (pDST) results in the central laboratory, with DNA sequencing as a reference standard.RESULTS: Of 413 multidrug-resistant TB (MDR-TB) patients tested using MTBDRsl and pDST, 389 (94.2%) were FQ-susceptible and 7 (1.7%) FQ-resistant, while 17 (4.1%) had an inconclusive MTBDRsl result. For SLI, 372 (90.1%) were susceptible, 5 (1.2%) resistant and 36 (8.7%) inconclusive. There were 9 (2.3%) FQ discordant pDST/MTBDRsl results, of which 3 revealed a mutation and 5 (1.3%) SLI discordant pDST/MTBDRsl results, none of which were mutants on sequencing. Among the 17 FQ- and SLI MTBDRsl-inconclusive samples, sequencing showed 1 FQ- and zero SLI-resistant results, similar to frequencies among the conclusive MTBDRsl. The majority of inconclusive MTBDRsl results were associated with low bacillary load samples (acid-fast bacilli smear-negative or scantily positive) compared to conclusive results (P &lt; 0.001).CONCLUSION: MTBDRsl can facilitate the rapid exclusion of FQ and SLI resistances for enrolment in clinical trials.</jats:p