Bioinformatic Modelling of SARS-CoV-2 Pandemic with a Focus on Country-Specific Dynamics

Background: One of the seminal events since 2019 has been the outbreak of the SARS-CoV-2 pandemic. Countries have adopted various policies to deal with it, but they also differ in their socio-geographical characteristics and the public health care facilities. Our study aimed to investigate differences between epidemiological parameters across countries.Method: The analysed data represents SARS-CoV-2 repository provided by the Johns Hopkins University. Separately for each country, we estimated recovery and mortality rates using the SIRD model applied to the first 30, 60, 150, and 300 days of the pandemic. Moreover, a mixture of normal distributions was fitted to the number of confirmed cases and deaths during the first 300 days. The estimates of peaks’ means and variances were used to identify countries with outlying parameters.Results: For 300 days Belgium, Cyprus, France, the Netherlands, Serbia, and the UK were classified as outliers by all three outlier detection methods. Yemen was classified as an outlier for each of the four considered timeframes, due to high mortality rates. During the first 300 days of the pandemic, the majority of countries underwent three peaks in the number of confirmed cases, except Australia and Kazakhstan with two peaks.Conclusions: Considering recovery and mortality rates we observed heterogeneity between countries. Liechtenstein was the “positive” outlier with low mortality rates and high recovery rates, at the opposite, Yemen represented a “negative” outlier with high mortality for all four considered periods and low recovery for 30 and 60 days.

Finite mixtures of normal distributions in the study of the error in altimetry

The modelling of the altimetric error is proposed by means of the mixture of normal distributions. This alternative allows to avoid the problems of lack of normality of the altimetric error and that have been indicated numerous times. The conceptual bases of the mixture of distributions are presented and its application is demonstrated with an applied example. In the example, the altimetric errors existing between a DEM with 5 × 5 m resolution and another DEM with 2 × 2 m resolution are modelled, which is considered as a reference. The application demonstrates the feasibility and power of analysis of the proposal made.

rGAI: An R package for fitting the generalised abundance index to seasonal count data

1. The Generalised Abundance Index (GAI) provides a useful tool for estimating relative population sizes and trends of seasonal invertebrates from species’ count data, and offers potential for inferring which external factors may influence phenology and demography through parametric descriptions of seasonal variation. 2. We provide an R package that extends previous software with the ability to include covariates when fitting parametric GAI models, where seasonal variation is described by either a mixture of Normal distributions or a stopover model which provides estimates of lifespan. The package also generalises the model to allow any number of broods/generations in the target population within a defined season. The option to perform bootstrapping, either parametrically or non-parametrically, is also provided. 3. The new package allows models to be far more flexible when describing seasonal variation, which may be dependent on site-specific environmental factors or consist of many broods/generations which may overlap, as demonstrated by two case studies. 4. Our open-source software, available at \href{https://github.com/calliste-fagard-jenkin/GAI}{https://github.com/calliste-fagard-jenkin/rGAI}, makes this extension widely and freely available, allowing the complexity of GAI models used by ecologists and applied statisticians to increase accordingly.

Bioinformatic Modelling of SARS-CoV-2 Pandemic With a Focus on Country-Specific Dynamics

One of the seminal events since 2019 has been the outbreak of the SARS-CoV-2 pandemic. Countries have adopted various policies to deal with it, but they also differ in their socio-geographical characteristics and in the public health care facilities. The aim of our study was to investigate differences between epidemiological parameters across countries. The analysed data represents SARS-CoV-2 repository provided by the Johns Hopkins University. Separately for each country we estimated recovery and mortality rates using the SIRD model applied to the first 30, 60, 150 and 300 days of the pandemic. Moreover, a mixture of normal distributions was fitted to the number of confirmed cases and deaths during the first 300 days. The estimates of peaks’ means and variances were used to identify countries with outlying parameters. For the period of 300 days Belgium, Cyprus, France, the Netherlands, Serbia and the UK were classified as outliers by all three outlier detection methods. Yemen was classified as an outlier for each of the four considered timeframes, due to high mortality rates. During the first 300 days of the pandemic the majority of countries underwent three peaks in the number of confirmed cases, except Australia and Kazakhstan with two peaks.

Normal approximation for mixtures of normal distributions and the evolution of phenotypic traits

Explicit bounds are given for the Kolmogorov and Wasserstein distances between a mixture of normal distributions, by which we mean that the conditional distribution given some $\sigma$ -algebra is normal, and a normal distribution with properly chosen parameter values. The bounds depend only on the first two moments of the first two conditional moments given the $\sigma$ -algebra. The proof is based on Stein’s method. As an application, we consider the Yule–Ornstein–Uhlenbeck model, used in the field of phylogenetic comparative methods. We obtain bounds for both distances between the distribution of the average value of a phenotypic trait over n related species, and a normal distribution. The bounds imply and extend earlier limit theorems by Bartoszek and Sagitov.

Using Mixture of Normal Distributions to Detect Treatment Effects when the Frequentist Method Fails

Background: Results from a clinical trial can either support the efficacy and safety of a new compound or fail to provide such evidence. One reason for ‘non[1]positive’ result is due to the underlying assumption of normality and homogeneity of variances, which are quite often violated when analyzing data from clinical trials, despite randomization. A question of interest is can we obtain more informative results when using mixture of normal distributions or linear models (MLMs) in such cases. Introduction: MLM can be used when traditional methods fail. MLMs “search” within the variability in data to identify components or subgroups of individuals (also known as latent classes) who have common intercepts and common slopes of change in a variable/endpoint of interest but whose intercepts and slopes are different from other subsets of patients. Thus, MLMs can be used to identify subgroups of patients exhibiting differential response to treatment within each treatment arm. The purpose of our study was to examine the usefulness of using MLM in such circumstances. Methods: Data of 155 subjects taken from a Multicenter, randomized, double blind, placebo controlled trial that evaluated the efficacy of Cpn10, administered twice weekly subcutaneously to treat Rheumatoid Arthritis was taken to evaluate the usefulness of MLM. The primary efficacy measure ACR20 was analyzed using a 3-step process: first, MLM was used to estimate RA duration using a 3-component model. The second step took the results of the first step to inform the logistic model and its analyses. Model was fitted with an intercept, MLM components, treatment arm, RA duration (linear and quadratic), dose response (modeled as an interaction effect), age and baseline weight. LOCF was used to impute for missing data. Data was analyzed using MLM and SAS v 9.0. Results: The model was a good fit to the data with a likelihood ratio significant at p=0.026, and a significant increase in the -2log L. We also observed low p-values for those variables that were non normal. Overall and for the 75 mg dose, Cpn 10 was efficacious relative to placebo, p<0.050. We also observed that dose response was significant at p><0.15 Conclusion: The use of MLM adds value because it can be used to understand the disease experience or the value of treatment when traditional statistical methods cannot. Key words: Mixture of linear models, normality, entropy.

Continuous review inventory model with lost sale reduction and ordering cost dependent on lead time for the mixtures of distributions

We consider a continuous review inventory system for inventory model involving lost sales reduction through capital investment cost function and the reduction of lead time further which reduces the ordering cost. To reduce the lost sales rate, two forms of capital investment cost function, viz. logarithmic and power are employed. Two relationships between ordering cost and lead time, viz. linear and logarithmic are considered. We develop four inventory models by taking different combinations of capital investment cost function and ordering cost lead time relationship. Objective of the study is to reduce the total related cost by simultaneously optimizing the order quantity, safety factor, fraction of the shortages during the stock-out period that will be lost and length of lead time. The lead time demand is assumed to follow a mixture of normal distributions. The optimal solution is derived by developing computer programs using the software MATLAB. We also provide four numerical examples to illustrate the models.