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Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the observed data are typically akin to a boundary value-type problem: we observe some of the dependent variables at given times, but we do not know the initial conditions. In this paper, we reformulate the classical susceptible–infectious–recovered system in terms of the number of detected positive infected cases at different times to yield what we term the observational model. We then prove the existence and uniqueness of a solution to the boundary value problem associated with the observational model and present a numerical algorithm to approximate the solution. This article is part of the theme issue ‘Technical challenges of modelling real-life epidemics and examples of overcoming these’.

Arrested replication forks, when restarted by homologous recombination, result in error-prone DNA syntheses and non-allelic homologous recombination. Fission yeast RTS1 is a model fork barrier used to probe mechanisms of recombination-dependent restart. RTS1 barrier activity is entirely dependent on the DNA binding protein Rtf1 and partially dependent on a second protein, Rtf2. Human RTF2 was recently implicated in fork restart, leading us to examine fission yeast Rtf2’s role in more detail. In agreement with previous studies, we observe reduced barrier activity upon rtf2 deletion. However, we identified Rtf2 to be physically associated with mRNA processing and splicing factors and rtf2 deletion to cause increased intron retention. One of the most affected introns resided in the rtf1 transcript. Using an intronless rtf1 we observed no reduction in RFB activity in the absence of Rtf2. Thus, Rtf2 is essential for correct rtf1 splicing to allow optimal RTS1 barrier activity.

Data compression of three-dimensional computational fluid dynamics (CFD) simulation data is crucial to allow effective data-streaming for drone navigation and control. This problem is computationally challenging due to the complexity of the geometrical features present in the CFD data, and cannot be tackled by standard compression techniques such as sphere-tree. In this report, we present two different methods based on octree and cuboid primitives to compress velocity isosurfaces and volumetric data in three dimensions. Our volume compression method achieves a 1400 compression rate of raw simulation data and allows parallel computing.

Crime data provides information on the nature and location of the crime but, in general, does not include information on the number of criminals operating in a region. By contrast, many approaches to crime reduction necessarily involve working with criminals or individuals at risk of engaging in criminal activity and so the dynamics of the criminal population is important. With this in mind, we develop a mechanistic, mathematical model which combines the number of crimes and number of criminals to create a dynamical system. Analysis of the model highlights a threshold for criminal efficiency, below which criminal numbers will settle to an equilibrium level that can be exploited to reduce crime through prevention. This efficiency measure arises from the initiation of new criminals in response to observation of criminal activity; other initiation routes - via opportunism or peer pressure - do not exhibit such thresholds although they do impact on the level of criminal activity observed. We used data from Cape Town, South Africa, to obtain parameter estimates and predicted that the number of criminals in the region is tending towards an equilibrium point but in a heterogeneous manner - a drop in the number of criminals from low crime neighbourhoods is being offset by an increase from high crime neighbourhoods.

SummaryBackgroundThe world is at the cusp of experiencing local/regional hot-spots and spikes of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which causes COVID-19 disease. We aimed to formulate an applicable epidemiological model to accurately predict and forecast the impact of local resurgence and outbreaks to guide the local healthcare demand and capacity, policy making, and public health decisions.MethodsThe model utilised the aggregated daily COVID-19 situation reports (including counts of daily admissions, discharges, and occupancy) from the local NHS hospitals and Covid-19 related weekly deaths in hospitals and other settings in Sussex (population 1-7M), Southeast England. These datasets corresponded to the first wave of COVID-19 infections from 24 March-15 June 2020. The counts of death registrations and regional population estimates were obtained from the Office of National Statistics. A novel epidemiological predictive and forecasting model was then derived based on the local/regional surveillance data. Through a rigorous inverse parameter inference approach, the model parameters were estimated by fitting the model to the data in an optimal sense and then subsequently validated to make predictions subject to 95% confidence.FindingsThe inferred parameters were physically reasonable and matched up to the widely used parameter values derived from the national datasets. Unlike other predictive models, which are restricted to a couple of days, our model can predict local hospital admissions, discharges (including deaths) and occupancy for the next 10, 20, and 30 days at the local level.InterpretationWe have demonstrated that by using local/regional data, our predictive and forecasting model can be utilised to guide the local healthcare demand and capacity, policy making, and public health decisions to mitigate the impact of COVID-19 on the local population. Understanding how future COVID-19 spikes/waves could possibly affect the regional populations empowers us to ensure the timely commissioning and organisation of services. Primary care and community services can be guided by the projected number of infectious and recovered patients and hospital admissions/discharges to project discharge pathways to bedded and community settings, thus allowing services to understand their likely load in future spikes/waves. The flexibility of timings in the model, in combination with other early warning systems, produces a timeframe for these services to prepare and isolate capacity for likely and potential demand within regional hospitals. The model also allows local authorities to plan potential mortuary capacity and understand the burden on crematoria and burial services. The model algorithms have been integrated into a web-based multi-institutional toolkit, which can be used by NHS hospitals, local authorities, and public health departments in other regions of the UK and elsewhere. The parameters, which are locally informed, form the basis of predicting and forecasting exercises accounting for different scenarios and impact of COVID-19 transmission.FundingThis study was supported by the Higher Education Innovation Fund through the University of Sussex (ECF, JVY, AMa). This work was partly supported by the Global Challenges Research Fund through the Engineering and Physical Sciences Research Council grant number EP/T00410X/1: UK-Africa Postgraduate Advanced Study Institute in Mathematical Sciences (AMa, ECF). ECF is supported by the Wellcome Trust grant number 204833/Z/16/Z.Research in contextEvidence before this studySince the beginning of the COVID-19 pandemic, healthcare managers and policy makers relied on epidemiological models based on national datasets to predict and mitigate the spread of the disease. The performance of these models has not always been validated against the available data, and they depend strongly on the values for the model parameters. Statistical models, e.g. those arising from time-series analysis, lack the temporal dynamics of the compartmentalised epidemiological model for the evolution of the disease and thus fail to capture the evolution far into the future with great accuracy. Compartmental models, on the other hand, capture the underlying dynamics of an infectious disease but typically use parameters estimated using datasets from other regions or countries, thus lacking the ability to capture local demographics and policy and therefore lack predicting local dynamics with accuracy.Added value of this studyAlthough our compartmental model follows standard SEIR-D model structure, the inference algorithm described and applied in this report is novel, along with the prediction technique used to validate the model. We checked bioRxiv, medRxiv, and arXiv up to the end of August 2020 using the terms “mathematical inference”, “COVID-19”, and “SIR” and found that there is a substantial use of Bayesian approaches to fit parameters but none that use the combination of statistical approaches with compartmental models, hence the originality of our work. We designed a compartmentalised epidemiological model that captures the basic dynamics of the COVID-19 pandemic and revolves around the data that are available at the local/regional level. We estimated all the parameters in the model using the local surveillance data, and in consequence, our parameters reflect the characteristics of the local population. Furthermore, we validated the predictive power of the model by using only a subset of the available data to fit the parameters. To the best of our knowledge, this is the first study which combines statistical approaches with a compartmental model and as such benefits greatly from the ability to predict and forecast much further into the future using the dynamical structure of the compartmental model with a relatively much higher accuracy than previously presented in the literature. This research sets the gold-standard benchmark by laying the framework for future adaptations to the model when more precise (and comprehensive) datasets are made available.Implications of all the available evidenceThe predictive power of our model outperforms previously available models for local forecasting of the impact of COVID-19. Using local models, rather than trying to use national models at a local scale, ensures that the model reflects the local demographics and provides reliable local-data-driven predictions to guide the local healthcare demand and capacity, policy making, and public health decisions to mitigate the impact of COVID-19 on the local population. Local authorities can use these results for the planning of local hospital demand as well as death management services by developing scenario-based analysis to which different values of the reproduction number R exiting a COVID-19 lockdown are assumed and results, such as maximum hospital occupancy, are compared to the first wave to establish a potential strain on resources. This can work as an early warning detection system to see what value of R that is currently followed, which in turn informs the relevant capacity and resources needed to mitigate the impact of COVID-19. The Web toolkit developed by us as a result of this study (https://alpha.halogen-health.org) demonstrates the predictive power of our model as well as its flexibility with the scenario-based analysis. Although our model is based on the data from Sussex, using similar variables/data from other regions in our model would derive respective COVID-19 model parameters, and thus enable similar scenario-based investigations to predict and forecast the impact of local resurgence to guide the local healthcare demand and capacity, policy making, and public health decisions.

This report addresses the construction of carbon fibre wing boxes and the problems associated with using carbon fibre sheets rather than individual carbon fibre tapes. In the case that the wing boxes are developable surfaces the lay up of carbon fibre sheets is straightforward, since the fibres can follow the contours of the surface without any need for shearing or extension of the fibres. To further expand the potential design space for the wing boxes, this report investigates the lay up of sheets over non-developable surfaces where some shearing of the sheet is required to achieve the desired results. In this report, three analytical approaches are considered, driven by the results from numerical studies on different surface geometries. Each of the approaches offers insights as to the type of geometric perturbations achievable when constrained by a maximum shear angle.

Investigational in vitro models that reflect the complexity of the interaction between the immune system and tumours are limited and difficult to establish. Herein, we present a platform to study the tumour-immune interaction using a co-culture between cancer spheroids and activated immune cells. An algorithm was developed for analysis of confocal images of the co-culture to evaluate the following quantitatively; immune cell infiltration, spheroid roundness and spheroid growth. As a proof of concept, the effect of the glucocorticoid stress hormone, cortisol was tested on 66CL4 co-culture model. Results were comparable to 66CL4 syngeneic in vivo mouse model undergoing psychological stress. Furthermore, administration of glucocorticoid receptor antagonists demonstrated the use of this model to determine the effect of treatments on the immune-tumour interplay. In conclusion, we provide a method of quantifying the interaction between the immune system and cancer, which can become a screening tool in immunotherapy design., Al-Hity et al present a platform to study the tumour-immune interaction using a co-culture between cancer spheroids and activated immune cells. They assess the effects of cortisol application to the culture model as proof-of-concept, which demonstrates the potential for this platform as a screening tool for immunotherapy design.

The essential Smc5/6 complex is required in response to replication stress and is best known for ensuring the fidelity of homologous recombination. Using single-molecule tracking in live fission yeast to investigate Smc5/6 chromatin association, we show that Smc5/6 is chromatin associated in unchallenged cells and this depends on the non-SMC protein Nse6. We define a minimum of two Nse6-dependent sub-pathways, one of which requires the BRCT-domain protein Brc1. Using defined mutants in genes encoding the core Smc5/6 complex subunits, we show that the Nse3 double-stranded DNA binding activity and the arginine fingers of the two Smc5/6 ATPase binding sites are critical for chromatin association. Interestingly, disrupting the single-stranded DNA (ssDNA) binding activity at the hinge region does not prevent chromatin association but leads to elevated levels of gross chromosomal rearrangements during replication restart. This is consistent with a downstream function for ssDNA binding in regulating homologous recombination.

Summary Local cell contraction pulses play important roles in tissue and cell morphogenesis. Here, we improve a chemo-optogenetic approach and apply it to investigate the signal network that generates these pulses. We use these measurements to derive and parameterize a system of ordinary differential equations describing temporal signal network dynamics. Bifurcation analysis and numerical simulations predict a strong dependence of oscillatory system dynamics on the concentration of GEF-H1, an Lbc-type RhoGEF, which mediates the positive feedback amplification of Rho activity. This prediction is confirmed experimentally via optogenetic tuning of the effective GEF-H1 concentration in individual living cells. Numerical simulations show that pulse amplitude is most sensitive to external inputs into the myosin component at low GEF-H1 concentrations and that the spatial pulse width is dependent on GEF-H1 diffusion. Our study offers a theoretical framework to explain the emergence of local cell contraction pulses and their modulation by biochemical and mechanical signals., Graphical Abstract, Highlights • Cell contraction dynamics are investigated via acute chemo-optogenetic perturbations • A theoretical model predicts GEF-H1-dependent switches in pulsatile Rho dynamics • Experimental manipulations of cytosolic GEF-H1 levels confirm model predictions • Local pulsatile dynamics are generated by coupling feedback regulation and diffusion, Kamps et al. derive a reaction-diffusion system that generates subcellular activity pulses of the cell contraction regulator Rho. System parameters are obtained by combining perturbation-response analyses with theoretical investigations. Multiple switches in activity dynamics, which are dependent on the positive feedback mediator GEF-H1, are predicted by theory and confirmed experimentally.

Replication forks restarted by homologous recombination are error prone and replicate both strands semi-conservatively using Pol δ. Here, we use polymerase usage sequencing to visualize in vivo replication dynamics of HR-restarted forks at an S. pombe replication barrier, RTS1, and model replication by Monte Carlo simulation. We show that HR-restarted forks synthesise both strands with Pol δ for up to 30 kb without maturing to a δ/ε configuration and that Pol α is not used significantly on either strand, suggesting the lagging strand template remains as a gap that is filled in by Pol δ later. We further demonstrate that HR-restarted forks progress uninterrupted through a fork barrier that arrests canonical forks. Finally, by manipulating lagging strand resection during HR-restart by deleting pku70, we show that the leading strand initiates replication at the same position, signifying the stability of the 3′ single strand in the context of increased resection., Replication forks that are stalled at obstacles on the DNA template can be restarted by homologous recombination. Here, the authors show replication dynamics during homologous recombination-dependent replication fork restart by combining polymerase usage sequencing and a Monte Carlo mathematical model.

The essential Smc5/6 complex is required in response to replication stress and is best known for ensuring the fidelity of homologous recombination. Using single-molecule tracking in live fission yeast to investigate Smc5/6 chromatin association, we show that Smc5/6 is chromatin associated in unchallenged cells and this depends on the non-SMC protein Nse6. We define a minimum of two Nse6-dependent sub-pathways, one of which requires the BRCT-domain protein Brc1. Using defined mutants in genes encoding the core Smc5/6 complex subunits we show that the Nse3 double-stranded DNA binding activity and the arginine fingers of the two Smc5/6 ATPase binding sites are critical for chromatin association. Interestingly, disrupting the ssDNA binding activity at the hinge region does not prevent chromatin association but leads to elevated levels of gross chromosomal rearrangements during replication restart. This is consistent with a downstream function for ssDNA binding in regulating homologous recombination.

In this study, we apply the Bayesian paradigm for parameter identification to a well-studied semi-linear reaction-diffusion system with activator-depleted reaction kinetics, posed on stationary as well as evolving domains. We provide a mathematically rigorous framework to study the inverse problem of finding the parameters of a reaction-diffusion system given a final spatial pattern. On the stationary domain the parameters are finite-dimensional, but on the evolving domain we consider the problem of identifying the evolution of the domain, i.e. a time-dependent function. Whilst others have considered these inverse problems using optimisation techniques, the Bayesian approach provides a rigorous mathematical framework for incorporating the prior knowledge on uncertainty in the observation and in the parameters themselves, resulting in an approximation of the full probability distribution for the parameters, given the data. Furthermore, using previously established results, we can prove well-posedness results for the inverse problem, using the well-posedness of the forward problem. Although the numerical approximation of the full probability is computationally expensive, parallelised algorithms make the problem solvable using high-performance computing.

Eduard Campillo-Funollet applies a set of data analysis tools to the study of the concept of home on the social network Twitter. The main goals are to understand how the concept of home is used in Twitter, and also to show the power of data analysis techniques to study problems in humanities and social sciences. The study focuses on a dataset of tweets that contain the word home. After a preliminary exploration of the data, the chapter presents an analysis of the word frequency in the tweets, a sentiment analysis, and an application of a word sense disambiguation algorithm.

This book is about the manifold interpretations and readings to which the concept of home lends itself. The authors show that home is a socially constructed phenomenon, with blurry boundaries and not free of conflict. It also shows that individuals, experiences, language, social and legal structures as well as history shape our conceptions of home, which are constantly shifting and being reconfigured. Because of its varied nature, home is a concept that allows for an interdisciplinary group of experts to provide an insight into how their ideas about such a quotidian concept can be shaped by their own work and explored through the lens of their disciplines.

We consider the problem of estimating the power and position of an unknown transmitter using only observations on the received power for several sensors, without any directional information. We describe several existing propagation models, and we compute the Fisher in- formation for the free-space loss model. For more complex model, we present some results using a Markov Chain Monte Carlo method, and we describe the application of a particle filter to estimate posterior distributions for the transmitter and channel characteristics.

Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the observed data is typically akin of a boundary value type problem: we observe some of the dependent variables at given times, but we do not know the initial conditions. In this paper, we reformulate the classical Susceptible-Infectious-Recovered system in terms of the number of detected positive infected cases at different times, we then prove the existence and uniqueness of a solution to the derived boundary value problem and then present a numerical algorithm to approximate the solution.