Global convergence of COVID-19 basic reproduction number and estimation from early-time SIR dynamics

The SIR ('susceptible-infectious-recovered') formulation is used to uncover the generic spread mechanisms observed by COVID-19 dynamics globally, especially in the early phases of infectious spread. During this early period, potential controls were not effectively put in place or enforced in many countries. Hence, the early phases of COVID-19 spread in countries where controls were weak offer a unique perspective on the ensemble-behavior of COVID-19 basic reproduction number Ro inferred from SIR formulation. The work here shows that there is global convergence (i.e., across many nations) to an uncontrolled Ro = 4.5 that describes the early time spread of COVID-19. This value is in agreement with independent estimates from other sources reviewed here and adds to the growing consensus that the early estimate of Ro = 2.2 adopted by the World Health Organization is low. A reconciliation between power-law and exponential growth predictions is also featured within the confines of the SIR formulation. The effects of testing ramp-up and the role of 'super-spreaders' on the inference of Ro are analyzed using idealized scenarios. Implications for evaluating potential control strategies from this uncontrolled Ro are briefly discussed in the context of the maximum possible infected fraction of the population (needed to assess health care capacity) and mortality (especially in the USA given diverging projections). Model results indicate that if intervention measures still result in Ro > 2.7 within 44 days after first infection, intervention is unlikely to be effective in general for COVID-19

Addressing mechanism bias in model-based impact forecasts of new tuberculosis vaccines

In tuberculosis (TB) vaccine development, multiple factors hinder the design and interpretation of the clinical trials used to estimate vaccine efficacy. The complex transmission chain of TB includes multiple routes to disease, making it hard to link the vaccine efficacy observed in a trial to specific protective mechanisms. Here, we present a Bayesian framework to evaluate the compatibility of different vaccine descriptions with clinical trial outcomes, unlocking impact forecasting from vaccines whose specific mechanisms of action are unknown. Applying our method to the analysis of the M72/AS01E vaccine trial -conducted on IGRA+ individuals- as a case study, we found that most plausible models for this vaccine needed to include protection against, at least, two over the three possible routes to active TB classically considered in the literature: namely, primary TB, latent TB reactivation and TB upon re-infection. Gathering new data regarding the impact of TB vaccines in various epidemiological settings would be instrumental to improve our model estimates of the underlying mechanisms

Bioinformaatika meetodid personaalses farmakoteraapias

Väitekirja elektrooniline versioon ei sisalda publikatsiooneKogutavate terviseandmete hulk kasvab kiiresti. Tänu neile andmetele on meditsiinilise ravi pakkumisel võimalik senisest enam arvesse võtta individuaalseid bioloogilisi andmeid. See doktoritöö käsitleb mitmeid personaalses meditsiinis esinevaid probleeme ja näitab, et ravi individualiseerimiseks kasutatavad andmed tulevad väga erinevatest allikatest. Inimestevahelised erinevused teevad ravimite metabolismi ennustamise keerukaks, siiski on ravi käigus kogutavad kontsentratsioonimõõtmised ravimiefekti hindamisel heaks allikaks. Me arendasime välja täppisdoseerimise tööriista, mis võimaldab vankomütsiini ravil vastsündinutele määrata ravi tõhustavat personaalseid doose kasutades selleks nende endi ravi käigus kogutud kontsentratsioone. Suurema osa ravimiteraapiate puhul ei ole võimalik pidevalt ravimi kontsentratsioone koguda. Nende ülejäänud ravimite puhul on heaks informatsiooniallikaks geneetika. Paljude ravimimetabolismiga seotud geneetiliste variantide mõju on piisav, et tingida muutuseid ravi läbiviimisel. Me uurisime geneetika ja ravimite kõrvalmõjude omavahelisi seoseid kasutades rahvastikupõhist lähenemist. See toetus Eesti Geenivaramu geeniandmetele ja teistele laiapõhjalistele terviseandmete registritele. Me leidsime ja valideerisime seose, et CTNNA3 geenis olev geenivariant tõstab oksikaamide ravil olevate inimeste jaoks kõrvalmõjude sagedust. Arvutuslik geneetika toetub kvantitatiivsetele meetoditele, millest kõige levinum on ülegenoomne assotsiatsiooni analüüs (GWAS). Sagedasti kasutatav GWASi järelsamm on aega nõudev GWASist ilmnenud p-väärtuste visuaalne hindamine teiste samas genoomi piirkonnas olevate geneetiliste variantide kontekstis. Selle sammu automatiseerimiseks arendasime me kaks tööriista, Manhattan Harvester ja Cropper, mis võimaldavad automaatselt huvipakkuvaid piirkondi tuvastada ja nende headust hinnata.The amount of collected health data is growing fast. Insights from these data allow using biological patient specifics to improve therapy management with further individualization. This thesis addresses problems in multiple sub-fields of personalised medicine and aims to illustrate that data for precision medicine emerges from different sources. Drug metabolism is difficult to predict because individual biological differences. Fortunately, drug concentrations are a good proxy for drug effect. To address the growing need for tools that allow on-line therapy adjustment based on individual concentrations we have developed and externally evaluated a precision dosing tool that allows individualised dosing of vancomycin in neonates. Other than drugs used in therapeutic drug monitoring, most pharmacotherapies can not rely on continuous concentration measurements but for such drugs genetics provides a valuable source of information for individualization. Effects of many genetic variants in drug metabolism pathways are often large enough to require changes in drug prescriptions or schedules. We have applied a population-based approach in testing relations between drug related adverse effects and genomic loci, and found and validated a novel variant in CTNNA3 gene that increases adverse drug effects in patients with oxicam prescriptions. This was done by leveraging the data in Estonian Genome Center and linking these to nation-wide electronic health data registries. Computational genetics relies on quantitative methods for which the most common is the genome-wide association analysis (GWAS). A common GWAS downstream step involves time-consuming visual assessment of the association study p-values in context with other variants in genomic vicinity. In order to streamline this step, we developed, Manhattan Harvester and Cropper, that allow for automated detection of peak areas and assign scores by emulating human evaluators.https://www.ester.ee/record=b524282

Reliable optimal controls for SEIR models in epidemiology

We present and compare two different optimal control approaches applied to SEIR models in epidemiology, which allow us to obtain some policies for controlling the spread of an epidemic. The first approach uses Dynamic Programming to characterise the value function of the problem as the solution of a partial differential equation, the Hamilton-Jacobi-Bellman equation, and derive the optimal policy in feedback form. The second is based on Pontryagin's maximum principle and directly gives open-loop controls, via the solution of an optimality system of ordinary differential equations. This method, however, may not converge to the optimal solution. We propose a combination of the two methods in order to obtain high-quality and reliable solutions. Several simulations are presented and discussed

Fully Bayesian experimental design for pharmacokinetic studies

Utility functions in Bayesian experimental design are usually based on the posterior distribution. When the posterior is found by simulation, it must be sampled from for each future data set drawn from the prior predictive distribution. Many thousands of posterior distributions are often required. A popular technique in the Bayesian experimental design literature to rapidly obtain samples from the posterior is importance sampling, using the prior as the importance distribution. However, importance sampling will tend to break down if there is a reasonable number of experimental observations and/or the model parameter is high dimensional. In this paper we explore the use of Laplace approximations in the design setting to overcome this drawback. Furthermore, we consider using the Laplace approximation to form the importance distribution to obtain a more efficient importance distribution than the prior. The methodology is motivated by a pharmacokinetic study which investigates the effect of extracorporeal membrane oxygenation on the pharmacokinetics of antibiotics in sheep. The design problem is to find 10 near optimal plasma sampling times which produce precise estimates of pharmacokinetic model parameters/measures of interest. We consider several different utility functions of interest in these studies, which involve the posterior distribution of parameter functions

Habitat Patch Occupancy Dynamics of Glaucous-winged Gulls (larus glaucescens) ii: A Continuous-time Model

The diurnal distribution and abundance dynamics of loafing Glaucous-winged Gulls (Larus glaucescens) were examined at Protection Island National Wildlife Refuge, Strait of Juan de Fuca, Washington. Asynchronous movement of gulls among three habitat patches dedicated to loafing was modeled as a function of environmental variables using differential equations. Multiple time scale analysis led to the derivation of algebraic models for habitat patch occupancy dynamics. The models were parameterized with hourly census data collected from each habitat patch, and the resulting model predictions were compared with observed census data. A four-compartment model explained 41% of the variability in the data. Models that predict the dynamics of organism distribution and abundance enhance understanding of the temporal and spatial organization of ecological systems, as well as the decision-making process in natural resource management. © 2005 Rocky Mountain Mathematics Consortium

Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

In this paper, we propose a model-based method for the reconstruction of not directly measured epidemiological data. To solve this task, we developed a generic optimization-based approach to compute unknown time-dependent quantities (such as states, inputs, and parameters) of discrete-time stochastic nonlinear models using a sequence of output measurements. The problem was reformulated as a stochastic nonlinear model predictive control computation, where the unknown inputs and parameters were searched as functions of the uncertain states, such that the model output followed the observations. The unknown data were approximated by Gaussian distributions. The predictive control problem was solved over a relatively long time window in three steps. First, we approximated the expected trajectories of the unknown quantities through a nonlinear deterministic problem. In the next step, we fixed the expected trajectories and computed the corresponding variances using closed-form expressions. Finally, the obtained mean and variance values were used as an initial guess to solve the stochastic problem. To reduce the estimated uncertainty of the computed states, a closed-loop input policy was considered during the optimization, where the state-dependent gain values were determined heuristically. The applicability of the approach is illustrated through the estimation of the epidemiological data of the COVID-19 pandemic in Hungary. To describe the epidemic spread, we used a slightly modified version of a previously published and validated compartmental model, in which the vaccination process was taken into account. The mean and the variance of the unknown data (e.g., the number of susceptible, infected, or recovered people) were estimated using only the daily number of hospitalized patients. The problem was reformulated as a finite-horizon predictive control problem, where the unknown time-dependent parameter, the daily transmission rate of the disease, was computed such that the expected value of the computed number of hospitalized patients fit the truly observed data as much as possible

A pitfall in the reconstruction of fibre ODFs using spherical deconvolution of diffusion MRI data

Diffusion weighted ( DW ) MRI facilitates non-invasive quantification of tissue microstructure and, in combination with appropriate signal processing, three-dimensional estimates of fibrous orientation. In recent years, attention has shifted from the diffusion tensor model, which assumes a unimodal Gaussian diffusion displacement profile to recover fibre orientation ( with various well-documented limitations ), towards more complex high angular resolution diffusion imaging ( HARDI ) analysis techniques. Spherical deconvolution ( SD ) approaches assume that the fibre orientation density function ( fODF ) within a voxel can be obtained by deconvolving a ‘common’ single fibre response function from the observed set of DW signals. In practice, this common response function is not known a priori and thus an estimated fibre response must be used. Here the establishment of this single-fibre response function is referred to as ‘calibration’. This work examines the vulnerability of two different SD approaches to inappropriate response function calibration: ( 1 ) constrained spherical harmonic deconvolution ( CSHD )—a technique that exploits spherical harmonic basis sets and ( 2 ) damped Richardson–Lucy ( dRL ) deconvolution—a technique based on the standard Richardson–Lucy deconvolution. Through simulations, the impact of a discrepancy between the calibrated diffusion profiles and the observed ( ‘Target’ ) DW-signals in both single and crossing-fibre configurations was investigated. The results show that CSHD produces spurious fODF peaks ( consistent with well known ringing artefacts ) as the discrepancy between calibration and target response increases, while dRL demonstrates a lower over-all sensitivity to miscalibration ( with a calibration response function for a highly anisotropic fibre being optimal ). However, dRL demonstrates a reduced ability to resolve low anisotropy crossing-fibres compared to CSHD. It is concluded that the range and spatial-distribution of expected single-fibre anisotropies within an image must be carefully considered to ensure selection of the appropriate algorithm, parameters and calibration. Failure to choose the calibration response function carefully may severely impact the quality of any resultant tractography

Development of Diffusion MRI Methodology to Quantify White Matter Integrity Underlying Post-Stroke Anomia

In 1909 German neurologist Korbinian Brodmann wrote “functional localization of the cerebral cortex without the lead of anatomy is impossible... In all domains, physiology has its firmest foundations in anatomy [1”. While histology is the current gold standard for studying brain microstructure, it is primarily a post-mortem technique that has an average resolution of one micrometer making it impractical for studying the entire brain. Diffusion Magnetic Resonance Imaging (dMRI) is ideally suited to study whole-brain tissue microstructure by sensitizing the MRI contrast to water diffusion, which has a length scale on the order of micrometers. Even though dMRI is applied clinically for the detection of acute ischemia, the relation between tissue microstructure and the dMRI signal is complex and not fully understood. The focus of this dissertation was the validation and development of a new biophysical model of the dMRI signal. Notwithstanding, it is important to keep in mind the potential clinical applications of these models, so in parallel we studied the relationship between white matter integrity and language impairments in post-stroke anomia. This application is of interest since response to language treatment is variable and it is currently difficult to predict which patients will benefit. A better understanding of the underlying brain damage could help inform on functionality and recovery potential. Our work resulted in 9 peer-reviewed papers in international journals and 13 abstracts in proceedings at national and international conferences. Using data collected from 32 chronic stroke patients with language impairments, we studied the relation between baseline naming impairments and microstructural integrity of the residual white matter. An existing dMRI technique, Diffusional Kurtosis Imaging (DKI), was used to assess the tissue microstructure along the length of two major white matter bundles: the Inferior Longitudinal Fasciculus (ILF) and the Superior Longitudinal Fasciculus (SLF). The frequency of semantic paraphasias was strongly associated with ILF axonal loss, whereas phonemic paraphasias were strongly associated with SLF axonal loss. This double dissociation between semantic and phonological processing is in agreement with the dual stream model of language processing and corroborates the concept that, during speech production, knowledge association (semantics) depends on the integrity of ventral pathways (ILF), whereas form encoding (phonological encoding) is more localized to dorsal pathways (SLF). Using a smaller dataset of 8 chronic stroke subjects whom underwent speech entrainment therapy, we assessed if naming improvements were supported by underlying changes in microstructure. Remarkably, we saw that a decrease in semantic errors during confrontational naming was related to a renormalization of the microstructure of the ILF. Together, these two studies support the idea that white matter integrity (in addition to regional gray matter damage) impacts baseline stroke impairments and disease progression. Acquiring accurate information about a patient’s linguistic disorder and the underlying neuropathology is often an integral part to developing an appropriate intervention strategy. However, DKI metrics describe the general physical process of diffusion, which can be difficult to interpret biologically. Different pathological processes could lead to similar DKI changes further complicating interpretation and possibly decreasing its specificity to disease. A multitude of biophysical models have been developed to improve the specificity of dMRI. Due to the complexity of biological tissue, assumptions are necessary, which can differ in stringency depending on the dMRI data at hand. One such assumption is that axons can be approximated by water confined to impermeable thin cylinders. In this dissertation, we provide evidence for this “stick model”. Using data from 2 healthy controls we show that the dMRI signal decay behaves as predicted from theory, particularly at strong diffusion weightings. This work validated the foundation of a biophysical model known as Fiber Ball Imaging (FBI), which allows for the calculation of the angular dependence of fiber bundles. Here, we extend FBI by introducing the technique Fiber Ball White Matter (FBWM) modeling that in addition provides estimations for the Axonal Water Fraction (AWF) and compartmental diffusivities. The ability to accurately estimate compartment specific diffusion dynamics could provide the opportunity to distinguish between different disease processes that affect axons differently than the extra-axonal environment (e.g. gliosis). Lastly, we were able to show that FBI data can also be used to calculate compartmental transverse relaxation times (T2). These metrics can be used as biomarkers, aid in the calculation of the myelin content, or be used to reduce bias in diffusion modeling metrics. Future work should focus on the application of FBI and FBWM to the study of white matter in post-stroke anomia. Since FBWM offers the advantage of isolating the diffusion dynamics of the intra- and extra- axonal environments, it could be used to distinguish between pathological processes such as glial cell infiltration and axonal degeneration. A more specific assessment of the structural integrity underlying anomia could provide information on an individual’s recovery potential and could pave the way for more targeted treatment strategies. The isolation of intra-axonal water is also beneficial for a technique known as dMRI tractography, which delineates the pathway of fiber bundles in the brain. dMRI tractography is a popular research tool for studying brain networks but it is notoriously challenging to do in post-stroke brains. In damaged brain tissue, the high extra-cellular water content masks the directionality of fibers; however, since FBI provides the orientational dependence of solely intra-axonal water, it is not affected by this phenomenon. It is important to understand that caution should be taken when applying biophysical models (FBWM/FBI vs. DKI) to the diseased brain as the validation we provided in this work was only for healthy white matter and these experiments should be repeated in pathological white matter