A Bose-Einstein Approach to the Random Partitioning of an Integer

Consider N equally-spaced points on a circle of circumference N. Choose at random n points out of $N$ on this circle and append clockwise an arc of integral length k to each such point. The resulting random set is made of a random number of connected components. Questions such as the evaluation of the probability of random covering and parking configurations, number and length of the gaps are addressed. They are the discrete versions of similar problems raised in the continuum. For each value of k, asymptotic results are presented when n,N both go to infinity according to two different regimes. This model may equivalently be viewed as a random partitioning problem of N items into n recipients. A grand-canonical balls in boxes approach is also supplied, giving some insight into the multiplicities of the box filling amounts or spacings. The latter model is a k-nearest neighbor random graph with N vertices and kn edges. We shall also briefly consider the covering problem in the context of a random graph model with N vertices and n (out-degree 1) edges whose endpoints are no more bound to be neighbors

qRT-PCR versus IFA-based quantification of male and female gametocytes in low-density Plasmodium falciparum infections and their relevance for transmission

Accurate quantification of female and male gametocytes and sex ratios in asymptomatic low-density malaria infections are important for assessing their transmission potential. Gametocytes often escape detection even by molecular methods, therefore ultralow gametocyte densities were quantified in large blood volumes.; Female and male gametocytes were quantified in 161 PCR-positive Plasmodium falciparum infections from a cross-sectional survey in Papua New Guinea. Ten-fold concentrated RNA from 800 µL blood was analyzed using female-specific pfs25 and male-specific pfmget or mssp qRT-PCR. Gametocyte sex ratios from qRT-PCR were compared with those from immunofluorescence assays (IFA).; Gametocytes were identified in 58% (93/161) P. falciparum-positive individuals. Mean gametocyte densities were frequently below 1 female and 1 male gametocyte/µL by qRT-PCR. The mean proportion of males was 0.39 (95% confidence interval, 0.33-0.44) by pfs25/pfmget qRT-PCR; this correlated well with IFA results (Pearsons r2 = 0.91; P < .001). A Poisson model fitted to our data predicted 16% P. falciparum-positive individuals that are likely to transmit, assuming at least 1 female and 1 male gametocyte per 2.5 µL mosquito bloodmeal.; Based on model estimates of female and male gametocytes per 2.5 µL blood, P. falciparum-positive individuals detected exclusively by ultrasensitive diagnostics are negligible for human-to-mosquito transmission.Estimating the transmission potential of ultralow-density malaria infections informs interventions. Almost all infections with ≥1 female and male gametocyte per 2.5 µL mosquito bloodmeal, and thus with highest likelihood of contributing to human-to-mosquito transmission, were detectable by standard molecular diagnostics

Efficacy and safety of primaquine and methylene blue for prevention of Plasmodium falciparum transmission in Mali: a phase 2, single-blind, randomised controlled trial.

BACKGROUND: Primaquine and methylene blue are gametocytocidal compounds that could prevent Plasmodium falciparum transmission to mosquitoes. We aimed to assess the efficacy and safety of primaquine and methylene blue in preventing human to mosquito transmission of P falciparum among glucose-6-phosphate dehydrogenase (G6PD)-normal, gametocytaemic male participants. METHODS: This was a phase 2, single-blind, randomised controlled trial done at the Clinical Research Centre of the Malaria Research and Training Centre (MRTC) of the University of Bamako (Bamako, Mali). We enrolled male participants aged 5-50 years with asymptomatic P falciparum malaria. G6PD-normal participants with gametocytes detected by blood smear were randomised 1:1:1:1 in block sizes of eight, using a sealed-envelope design, to receive either sulfadoxine-pyrimethamine and amodiaquine, sulfadoxine-pyrimethamine and amodiaquine plus a single dose of 0·25 mg/kg primaquine, dihydroartemisinin-piperaquine, or dihydroartemisinin-piperaquine plus 15 mg/kg per day methylene blue for 3 days. Laboratory staff, investigators, and insectary technicians were masked to the treatment group and gametocyte density of study participants. The study pharmacist and treating physician were not masked. Participants could request unmasking. The primary efficacy endpoint, analysed in all infected patients with at least one infectivity measure before and after treatment, was median within-person percentage change in mosquito infectivity 2 and 7 days after treatment, assessed by membrane feeding. This study is registered with ClinicalTrials.gov, number NCT02831023. FINDINGS: Between June 27, 2016, and Nov 1, 2016, 80 participants were enrolled and assigned to the sulfadoxine-pyrimethamine and amodiaquine (n=20), sulfadoxine-pyrimethamine and amodiaquine plus primaquine (n=20), dihydroartemisinin-piperaquine (n=20), or dihydroartemisinin-piperaquine plus methylene blue (n=20) groups. Among participants infectious at baseline (54 [68%] of 80), those in the sulfadoxine-pyrimethamine and amodiaquine plus primaquine group (n=19) had a median 100% (IQR 100 to 100) within-person reduction in mosquito infectivity on day 2, a larger reduction than was noted with sulfadoxine-pyrimethamine and amodiaquine alone (n=12; -10·2%, IQR -143·9 to 56·6; p<0·0001). The dihydroartemisinin-piperaquine plus methylene blue (n=11) group had a median 100% (IQR 100 to 100) within-person reduction in mosquito infectivity on day 2, a larger reduction than was noted with dihydroartemisinin-piperaquine alone (n=12; -6·0%, IQR -126·1 to 86·9; p<0·0001). Haemoglobin changes were similar between gametocytocidal arms and their respective controls. After exclusion of blue urine, adverse events were similar across all groups (59 [74%] of 80 participants had 162 adverse events overall, 145 [90%] of which were mild). INTERPRETATION: Adding a single dose of 0·25 mg/kg primaquine to sulfadoxine-pyrimethamine and amodiaquine or 3 days of 15 mg/kg per day methylene blue to dihydroartemisinin-piperaquine was highly efficacious for preventing P falciparum transmission. Both primaquine and methylene blue were well tolerated. FUNDING: Bill & Melinda Gates Foundation, European Research Council

Markers of sulfadoxine-pyrimethamine resistance in Eastern Democratic Republic of Congo; implications for malaria chemoprevention

Background Sulfadoxine–pyrimethamine (SP) is a cornerstone of malaria chemoprophylaxis and is considered for programmes in the Democratic Republic of Congo (DRC). However, SP efficacy is threatened by drug resistance, that is conferred by mutations in the dhfr and dhps genes. The World Health Organization has specified that intermittent preventive treatment for infants (IPTi) with SP should be implemented only if the prevalence of the dhps K540E mutation is under 50%. There are limited current data on the prevalence of resistance-conferring mutations available from Eastern DRC. The current study aimed to address this knowledge gap. Methods Dried blood-spot samples were collected from clinically suspected malaria patients [outpatient department (OPD)] and pregnant women attending antenatal care (ANC) in four sites in North and South Kivu, DRC. Quantitative PCR (qPCR) was performed on samples from individuals with positive and with negative rapid diagnostic test (RDT) results. Dhps K450E and A581G and dhfr I164L were assessed by nested PCR followed by allele-specific primer extension and detection by multiplex bead-based assays. Results Across populations, Plasmodium falciparum parasite prevalence was 47.9% (1160/2421) by RDT and 71.7 (1763/2421) by qPCR. Median parasite density measured by qPCR in RDT-negative qPCR-positive samples was very low with a median of 2.3 parasites/µL (IQR 0.5–25.2). Resistance genotyping was successfully performed in RDT-positive samples and RDT-negative/qPCR-positive samples with success rates of 86.2% (937/1086) and 55.5% (361/651), respectively. The presence of dhps K540E was high across sites (50.3–87.9%), with strong evidence for differences between sites (p < 0.001). Dhps A581G mutants were less prevalent (12.7–47.2%). The dhfr I164L mutation was found in one sample. Conclusions The prevalence of the SP resistance marker dhps K540E exceeds 50% in all four study sites in North and South Kivu, DRC. K540E mutations regularly co-occurred with mutations in dhps A581G but not with the dhfr I164L mutation. The current results do not support implementation of IPTi with SP in the study area

A randomized feasibility trial comparing four antimalarial drug regimens to induce Plasmodium falciparum gametocytemia in the controlled human malaria infection model.

Background: Malaria elimination strategies require a thorough understanding of parasite transmission from human to mosquito. A clinical model to induce gametocytes to understand their dynamics and evaluate transmission-blocking interventions (TBI) is currently unavailable. Here, we explore the use of the well-established Controlled Human Malaria Infection model (CHMI) to induce gametocyte carriage with different antimalarial drug regimens. Methods: In a single centre, open-label randomised trial, healthy malaria-naive participants (aged 18–35 years) were infected with Plasmodium falciparum by bites of infected Anopheles mosquitoes. Participants were randomly allocated to four different treatment arms (n = 4 per arm) comprising low-dose (LD) piperaquine (PIP) or sulfadoxine-pyrimethamine (SP), followed by a curative regimen upon recrudescence. Male and female gametocyte densities were determined by molecular assays. Results: Mature gametocytes were observed in all participants (16/16, 100%). Gametocytes appeared 8.5–12 days after the first detection of asexual parasites. Peak gametocyte densities and gametocyte burden was highest in the LD-PIP/SP arm, and associated with the preceding asexual parasite biomass (p=0.026). Male gametocytes had a mean estimated circulation time of 2.7 days (95% CI 1.5–3.9) compared to 5.1 days (95% CI 4.1–6.1) for female gametocytes. Exploratory mosquito feeding assays showed successful sporadic mosquito infections. There were no serious adverse events or significant differences in the occurrence and severity of adverse events between study arms (p=0.49 and p=0.28). Conclusions: The early appearance of gametocytes indicates gametocyte commitment during the first wave of asexual parasites emerging from the liver. Treatment by LD-PIP followed by a curative SP regimen, results in the highest gametocyte densities and the largest number of gametocyte-positive days. This model can be used to evaluate the effect of drugs and vaccines on gametocyte dynamics, and lays the foundation for fulfilling the critical unmet need to evaluate transmission-blocking interventions against falciparum malaria for downstream selection and clinical development. Funding: Funded by PATH Malaria Vaccine Initiative (MVI). Clinical trial number: NCT02836002

Persistence of mRNA indicative of Plasmodium falciparum ring-stage parasites 42 days after artemisinin and non-artemisinin combination therapy in naturally infected Malians.

BACKGROUND: Malaria control in sub-Saharan Africa relies upon prompt case management with artemisinin-based combination therapy (ACT). Ring-stage parasite mRNA, measured by sbp1 quantitative reverse-transcriptase PCR (qRT-PCR), was previously reported to persist after ACT treatment and hypothesized to reflect temporary arrest of the growth of ring-stage parasites (dormancy) following exposure to artemisinins. Here, the persistence of ring-stage parasitaemia following ACT and non-ACT treatment was examined. METHODS: Samples were used from naturally infected Malian gametocyte carriers who received dihydroartemisinin-piperaquine (DP) or sulfadoxine-pyrimethamine (SP-AQ) with or without gametocytocidal drugs. Gametocytes and ring-stage parasites were quantified by qRT-PCR during 42 days of follow-up. RESULTS: At baseline, 89% (64/73) of participants had measurable ring-stage parasite mRNA. Following treatment, the proportion of ring-stage parasite-positive individuals and estimated densities declined for all four treatment groups. Ring-stage parasite prevalence and density was generally lower in arms that received DP compared to SP-AQ. This finding was most apparent days 1, 2, and 42 of follow-up (p < 0.01). Gametocytocidal drugs did not influence ring-stage parasite persistence. Ring-stage parasite density estimates on days 14 and 28 after initiation of treatment were higher among individuals who subsequently experienced recurrent parasitaemia compared to those who remained free of parasites until day 42 after initiation of treatment (pday 14 = 0.011 and pday 28 = 0.068). No association of ring-stage persistence with gametocyte carriage was observed. CONCLUSIONS: The current findings of lower ring-stage persistence after ACT without an effect of gametocytocidal partner drugs affirms the use of sbp1 as ring-stage marker. Lower persistence of ring-stage mRNA after ACT treatment suggests the marker may not reflect dormant parasites whilst it was predictive of re-appearance of parasitaemia

Quantification of female and male Plasmodium falciparum gametocytes by reverse transcriptase quantitative PCR

The transmission of malaria parasites depends on the presence of sexual stages (gametocytes) in the blood, making the ratio and densities of female and male gametocytes important determinants of parasite fitness. This manuscript describes the development of reverse transcriptase quantitative PCR (RT-qPCR) assays to separately quantify mature female and male gametocytes of the human malaria parasite Plasmodium falciparum, and reveals that Pfs25 mRNA is expressed only in female gametocytes. The female (Pfs25) and male (Pfs230p) gametocyte specific RT-qPCR assays have lower detection limits of 0.3 female and 1.8 male gametocytes per microlitre of blood, respectively, making them more sensitive than microscopy. Accurate quantification of the ratio and densities of female and male gametocytes will increase understanding of P. falciparum transmission and improve the evaluation of transmission blocking interventions