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In a singularly perturbed limit, we analyse the existence and linear stability of steady-state hotspot solutions for an extension of the 1-D three-component reaction-diffusion (RD) system formulated and studied numerically in Jones et. al. [Math. Models. Meth. Appl. Sci., 20, Suppl., (2010)], which models urban crime with police intervention. In our extended RD model, the field variables are the attractiveness field for burglary, the criminal population density and the police population density. Our model includes a scalar parameter that determines the strength of the police drift towards maxima of the attractiveness field. For a special choice of this parameter, we recover the ‘cops-on-the-dots’ policing strategy of Jones et. al., where the police mimic the drift of the criminals towards maxima of the attractiveness field. For our extended model, the method of matched asymptotic expansions is used to construct 1-D steady-state hotspot patterns as well as to derive nonlocal eigenvalue problems (NLEPs) that characterise the linear stability of these hotspot steady states to
(1) timescale instabilities. For a cops-on-the-dots policing strategy, we prove that a multi-hotspot steady state is linearly stable to synchronous perturbations of the hotspot amplitudes. Alternatively, for asynchronous perturbations of the hotspot amplitudes, a hybrid analytical–numerical method is used to construct linear stability phase diagrams in the police vs. criminal diffusivity parameter space. In one particular region of these phase diagrams, the hotspot steady states are shown to be unstable to asynchronous oscillatory instabilities in the hotspot amplitudes that arise from a Hopf bifurcation. Within the context of our model, this provides a parameter range where the effect of a cops-on-the-dots policing strategy is to only displace crime temporally between neighbouring spatial regions. Our hybrid approach to study the NLEPs combines rigorous spectral results with a numerical parameterisation of any Hopf bifurcation threshold. For the cops-on-the-dots policing strategy, our linear stability predictions for steady-state hotspot patterns are confirmed from full numerical PDE simulations of the three-component RD system.
Domestic dogs display complex roaming behaviours, which need to be captured to more realistically model the spread of rabies. We have previously shown that roaming behaviours of domestic dogs can be categorised as stay-at-home, roamer and explorer in the Northern Peninsular Area (NPA), Queensland, Australia. These roaming behaviours are likely to cause heterogeneous contact rates that influence the speed or pattern of rabies spread in a dog population. The aim of this study was to define contact spatial kernels using the overlap of individual dog utilisation distributions to describe the daily probability of contact between pairs of dogs exhibiting these three a priori roaming behaviours. We further aimed to determine if the kernels lead to different predicted rabies outbreaks (outbreak duration and number of rabid dogs) by incorporating the spatial kernels into a previously developed rabies spread model for the NPA. Spatial kernels created with both dogs in a pair being explorers or one dog explorer and one dog roamer (who roamed away from their residence) produced short but large outbreaks compared with spatial kernels with at least one stay-at-home dog. Outputs from this model incorporating heterogeneous contacts demonstrate how roaming behaviours influence disease spread in domestic dog populations.
Improving geolocation accuracy in text data has long been a goal of automated text processing. We depart from the conventional method and introduce a two-stage supervised machine-learning algorithm that evaluates each location mention to be either correct or incorrect. We extract contextual information from texts, i.e., N-gram patterns for location words, mention frequency, and the context of sentences containing location words. We then estimate model parameters using a training data set and use this model to predict whether a location word in the test data set accurately represents the location of an event. We demonstrate these steps by constructing customized geolocation event data at the subnational level using news articles collected from around the world. The results show that the proposed algorithm outperforms existing geocoders even in a case added post hoc to test the generality of the developed algorithm.
This research aims to explore the submerged landscapes of the Pilbara of western Australia, using predictive archaeological modelling, airborne LiDAR, marine acoustics, coring and diver survey. It includes excavation and geophysical investigation of a submerged shell midden in Denmark to establish guidelines for the underwater discovery of such sites elsewhere.
Good education requires student experiences that deliver lessons about practice as well as theory and that encourage students to work for the public good—especially in the operation of democratic institutions (Dewey 1923; Dewy 1938). We report on an evaluation of the pedagogical value of a research project involving 23 colleges and universities across the country. Faculty trained and supervised students who observed polling places in the 2016 General Election. Our findings indicate that this was a valuable learning experience in both the short and long terms. Students found their experiences to be valuable and reported learning generally and specifically related to course material. Postelection, they also felt more knowledgeable about election science topics, voting behavior, and research methods. Students reported interest in participating in similar research in the future, would recommend other students to do so, and expressed interest in more learning and research about the topics central to their experience. Our results suggest that participants appreciated the importance of elections and their study. Collectively, the participating students are engaged and efficacious—essential qualities of citizens in a democracy.
There is strong evidence that people born in winter and in spring have a small increased risk of schizophrenia. As this ‘season of birth’ effect underpins some of the most influential hypotheses concerning potentially modifiable risk exposures, it is important to exclude other possible explanations for the phenomenon.
Here we sought to determine whether the season of birth effect reflects gene-environment confounding rather than a pathogenic process indexing environmental exposure. We directly measured, in 136 538 participants from the UK Biobank (UKBB), the burdens of common schizophrenia risk alleles and of copy number variants known to increase the risk for the disorder, and tested whether these were correlated with a season of birth.
Neither genetic measure was associated with season or month of birth within the UKBB sample.
As our study was highly powered to detect small effects, we conclude that the season of birth effect in schizophrenia reflects a true pathogenic effect of environmental exposure.
Access to acute and emergency care is essential when we are ill or injured, but the costs are significant. How can we make services more efficient and effective? This thought-provoking text provides twenty case studies detailing successful innovations to enhance value, including telehealth, observation medicine, high utilizer programs, and the use of informatics to improve clinical decision support. A detailed history of system developments over the last fifty years in the US and internationally is provided, and subjects including measurement and quality improvement, volume versus value based care, and emergency department crowding are discussed. This book is an ideal way for emergency physicians and healthcare managers to explore new ideas and enhance the quality of care in their area.
This special issue of the European journal of applied mathematics features research articles that involve the application of mathematical methodologies to the modelling of a broad range of problems related to crime and security. Some specific topics in this issue include recent developments in mathematical models of residential burglary, a dynamical model for the spatial spread of riots initiated by some triggering event, the analysis and development of game-theoretic models of crime and conflict, the study of statistically based models of insurgent activity and terrorism using real-world data sets, models for the optimal strategy of police deployment under realistic constraints, and a model of cyber crime as related to the study of spiking behaviour in social network cyberspace communications. Overall, the mathematical and computational methodologies employed in these studies are as diverse as the specific applications themselves and the scales (spatial or otherwise) to which they are applied. These methodologies range from statistical and stochastic methods based on maximum likelihood methods, Bayesian equilibria, regression analysis, self-excited Hawkes point processes, agent-based random walk models on networks, to more traditional applied mathematical methods such as dynamical systems and stability theory, the theory of Nash equilibria, rigorous methods in partial differential equations and travelling wave theory, and asymptotic methods that exploit disparate space and time scales.
Blood culture collection practices that reduce contamination, such as sterile blood culture collection kits and phlebotomy teams, increase up-front costs for collecting cultures but may lead to net savings by eliminating downstream costs associated with contamination. The study objective was to compare overall hospital costs associated with 3 collection strategies: usual care, sterile kits, and phlebotomy teams.
This analysis was conducted from the perspective of a hospital leadership team selecting a blood culture collection strategy for an adult emergency department (ED) with 8,000 cultures drawn annually.
Total hospital costs associated with 3 strategies were compared: (1) usual care, with nurses collecting cultures without a standardized protocol; (2) sterile kits, with nurses using a dedicated sterile collection kit; and (3) phlebotomy teams, with cultures collected by laboratory-based phlebotomists. In the base case, contamination rates associated with usual care, sterile kits, and phlebotomy teams were assumed to be 4.34%, 1.68%, and 1.10%, respectively. Total hospital costs included costs of collecting cultures and hospitalization costs according to culture results (negative, true positive, and contaminated).
Compared with usual care, annual net savings using the sterile kit and phlebotomy team strategies were $483,219 and $288,980, respectively. Both strategies remained less costly than usual care across a broad range of sensitivity analyses.
EDs with high blood culture contamination rates should strongly consider evidence-based strategies to reduce contamination. In addition to improving quality, implementing a sterile collection kit or phlebotomy team strategy is likely to result in net cost savings.