Distribution of clones among hosts for the lizard malaria parasite Plasmodium mexicanum

Background Malaria parasites reproduce asexually, leading to the production of large numbers of genetically identical parasites, here termed a clonal line or clone. Infected hosts may harbor one or more clones, and the number of clones in a host is termed multiplicity of infection (MOI). Understanding the distribution of parasite clones among hosts can shed light on the processes shaping this distribution and is important for modeling MOI. Here, I determine whether the distribution of clones of the lizard malaria parasite Plasmodium mexicanum differ significantly from statistical distributions commonly used to model MOI and logical extensions of these models. Methods The number of clones per infection was assessed using four microsatellite loci with the maximum number of alleles at any one locus used as a simple estimate of MOI for each infection. I fit statistical models (Poisson, negative binomial, zero-inflated models) to data from four individual sites to determine a best fit model. I also simulated the number of alleles per locus using an unbiased estimate of MOI to determine whether the simple (but potentially biased) method I used to estimate MOI influenced model fit. Results The distribution of clones among hosts at individual sites differed significantly from traditional Poisson and negative binomial distributions, but not from zero-inflated modifications of these distributions. A consistent excess of two-clone infections and shortage of one-clone infections relative to all fit distributions was also observed. Any bias introduced by the simple method for estimating of MOI did not appear to qualitatively alter the results. Conclusions The statistical distributions used to model MOI are typically zero-truncated; truncating the Poisson or zero-inflated Poisson yield the same distribution, so the reasonable fit of the zero-inflated Poisson to the data suggests that the use of the zero-truncated Poisson in modeling is adequate. The improved fit of zero-inflated distributions relative to standard distributions may suggest that only a portion of the host population is located in areas suitable for transmission even at small sites (<1 ha). Collective transmission of clones and premunition may also contribute to deviations from standard distributions.

On Approximation of the Panjer Distribution by the Poisson and Binomial Distributions

The aim of this paper is to approximate the panjer distribution by the poisson and binomial distributions, where each bound is obtained by using the z-function and the Stein-Chen identity. For these bounds, it is indicated that a result of each of the Poisson and Binomial approximations yields a good approximation if both α and λ are small.

Does apple canker develop independently on leaf scars of a single apple shoot?

European apple canker, caused by Neonectria ditissima, causes serious damage to apple trees, particularly young trees. Canker management is difficult because of the limited availability of effective fungicides, the long latency period, inoculum abundance and host resistance in commercial cultivars as well as the need for costly manual pruning interventions. To understand disease aggregation for more effective pruning management, we assessed whether canker infection and subsequent lesion development on leaf scars are independent from each other on the same shoot. Four inoculation experiments were conducted: one in glasshouse, and three in orchards. On each shoot, 10 consecutive leaf scars were inoculated and assessed for visible cankers over time in situ. Number of cankers developed per shoot as well as spatial distribution of these cankers within a shoot was statistically analysed. Most data of the number of visible canker lesions on a single shoot failed to fit binomial distributions (indicator for independence) and were fitted much better by beta binomial distributions. In a number of cases (4–20%), there appeared to be positive association between lesion development on neighbouring leaf scars. However, in one experiment where laboratory incubation and isolation of N. ditissima from inoculated but asymptomatic leaf scars (after eight months’ field incubation) were used the results suggested independence of canker development on a single shoot. We conclude that apparent aggregation of canker lesions on individual shoots is likely to originate from host responses. Such aggregation of canker lesions on individual shoots should be taken into consideration for field disease assessment and management.

Exploring secondary SARS-CoV-2 transmission from asymptomatic cases using contact tracing data

Background Individuals with asymptomatic severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) infection can propagate the virus unknowingly and thus have been a focus of public health attentions since the early stages of the pandemic. Understanding viral transmissibility among asymptomatic individuals is critical for successful control of coronavirus disease 2019 (COVID-19). The present study aimed to understand SARS-CoV-2 transmissibility among young asymptomatic individuals and to assess whether symptomatology was associated with transmission of symptomatic vs. asymptomatic infections. Methods We analyzed one of the first-identified clusters of SARS-CoV-2 infections with multiple chains of transmission that occurred among university students in March 2020 in Kyoto prefecture, Japan, using discrete and two-type branching process models. Assuming that the number of secondary cases resulting from either primary symptomatic or asymptomatic cases independently followed negative binomial distributions, we estimated the relative reproduction numbers of an asymptomatic case compared with a symptomatic case. To explore the potential association between symptomatology and transmission of symptomatic vs. asymptomatic incident infections, we also estimated the proportion of secondary symptomatic cases produced by primary symptomatic and asymptomatic cases. Results The reproduction number for a symptomatic primary case was estimated at 1.14 (95% confidence interval [CI]: 0.61–2.09). The relative reproduction number for asymptomatic cases was estimated at 0.19 (95% CI: 0.03–0.66), indicating that asymptomatic primary cases did not result in sufficient numbers of secondary infections to maintain chains of transmission. There was no apparent tendency for symptomatic primary cases to preferentially produce symptomatic secondary cases. Conclusions Using data from a transmission network during the early epidemic in Japan, we successfully estimated the relative transmissibility of asymptomatic cases of SARS-CoV-2 infection at 0.22. These results suggest that contract tracing focusing on symptomatic index cases may be justified given limited testing capacity.

On the Raşa Inequality for Higher Order Convex Functions

We study the following $$(q-1)$$ ( q - 1 ) th convex ordering relation for qth convolution power of the difference of probability distributions $$\mu $$ μ and $$\nu $$ ν $$\begin{aligned} (\nu -\mu )^{*q}\ge _{(q-1)cx} 0 , \quad q\ge 2, \end{aligned}$$ ( ν - μ ) ∗ q ≥ ( q - 1 ) c x 0 , q ≥ 2 , and we obtain the theorem providing a useful sufficient condition for its verification. We apply this theorem for various families of probability distributions and we obtain several inequalities related to the classical interpolation operators. In particular, taking binomial distributions, we obtain a new, very short proof of the inequality given recently by Abel and Leviatan (2020).

ARRIVAL PATTERNS AND TRAFFIC FLOW CHARACTERISTICS AT SIGNALIZED INTERSECTIONS

Traffic arrivals at signal intersection approaches is inherently stochastic. This variability is typically reflected by I-ratio and there is a general consensus that the presence or absence of nearby upstream signal affects Variance to Mean Ratio (I-ratio). However, the effect of time resolution on arrival variability and the interaction effect between upstream signal and time resolution is yet to be examined in detail. This can lead to model misspecification and invariably, erroneous outcomes. This work examines the effect of time resolution and intersection type and their interaction on I-ratio and the resultant probability distributions. Traffic arrivals were measured at high time resolution- 10 seconds interval and then aggregated to lower time resolutions (30-150 seconds) at six intersections. Spectral density analysis showed statistically significant periodicity, specifically at 30 seconds interval with p-values < 0.0001 at all connected intersections while observations at isolated intersections lacked periodicity. Two-way ANOVA using I-ratio as the dependent variable and intersection type and time-resolution as the independent variables was performed. Statistically significant effect with F-value 8.606 at p-value < 0.0001 and R2 value 0.32 were observed. Intersection type, time resolution and the interaction between them were statistically significant, with p-values 0.002, < 0.0001 and 0.000 respectively. The combined effect of these factors led to a wide I-ratio range of 0.37-9.2. Negative Binomial, Poisson, and Binomial distributions represented 76.4, 20.4 and 4.2% of all I-ratios observed. Therefore, in contrast to literature which recommends Poisson, Negative Binomial may be a better suited probability distribution for traffic arrivals.

A Stochastic Condensation Mechanism for Inducing Underdispersion in Count Models

It is quite easy to stochastically distort an original count variable to obtain a new count variable with relatively more variability than in the original variable. Many popular overdispersion models (variance greater than mean) can indeed be obtained by mixtures, compounding or randomlystopped sums. There is no analogous stochastic mechanism for the construction of underdispersed count variables (variance less than mean), starting from an original count distribution of interest. This work proposes a generic method to stochastically distort an original count variable to obtain a new count variable with relatively less variability than in the original variable. The proposed mechanism, termed condensation, attracts probability masses from the quantiles in the tails of the original distribution and redirect them toward quantiles around the expected value. If the original distribution can be simulated, then the simulation of variates from a condensed distribution is straightforward. Moreover, condensed distributions have a simple mean-parametrization, a characteristic useful in a count regression context. An application to the negative binomial distribution resulted in a distribution allowing under, equi and overdispersion. In addition to graphical insights, fields of applications of special cases of condensed Poisson and condensed negative binomial distributions were pointed out as an indication of the potential of condensation for a flexible analysis of count data

Optimal Probabilistic Scheduling in Time Slotted Multiple Access

This paper presents an efficient scheduling model for the delivery of sensing data in networks that use time division multiple access. The model is capable of achieving the optimal solution in terms of total delivery time, given certain constraints on radio resources. The proposed solution adopts a probabilistic approach which is based on a problem formulation utilizing chained binomial distributions.

Statistical models for identifying frequent hitters in high throughput screening

High throughput screening (HTS) interrogates compound libraries to find those that are “active” in an assay. To better understand compound behavior in HTS, we assessed an existing binomial survivor function (BSF) model of “frequent hitters” using 872 publicly available HTS data sets. We found large numbers of “infrequent hitters” using this model leading us to reject the BSF for identifying “frequent hitters.” As alternatives, we investigated generalized logistic, gamma, and negative binomial distributions as models for compound behavior. The gamma model reduced the proportion of both frequent and infrequent hitters relative to the BSF. Within this data set, conclusions about individual compound behavior were limited by the number of times individual compounds were tested (1–1613 times) and disproportionate testing of some compounds. Specifically, most tests (78%) were on a 309,847-compound subset (17.6% of compounds) each tested ≥ 300 times. We concluded that the disproportionate retesting of some compounds represents compound repurposing at scale rather than drug discovery. The approach to drug discovery represented by these 872 data sets characterizes the assays well by challenging them with many compounds while each compound is characterized poorly with a single assay. Aggregating the testing information from each compound across the multiple screens yielded a continuum with no clear boundary between normal and frequent hitting compounds.