Process modelling of NHS cardiovascular waiting lists in response to the COVID-19 pandemic.

Objective: To model the referral, diagnostic and treatment pathway for cardiovascular disease (CVD) in the English National Health Service (NHS) to provide commissioners and managers with a methodology to optimise patient flow and reduce waiting lists.

Study Design: A systems dynamics approach modelling the CVD healthcare system in England. The model is designed to capture current and predict future states of waiting lists.

A new phase model of the spatiotemporal relationships between three circadian oscillators in the brainstem.

Analysis of ex vivo Per2 bioluminescent rhythm previously recorded in the mouse dorsal vagal complex reveals a characteristic phase relationship between three distinct circadian oscillators. These signals represent core clock gene expression in the area postrema (AP), the nucleus of the solitary tract (NTS) and the ependymal cells surrounding the 4th ventricle (4Vep). Initially, the data suggests a consistent phasing in which the AP peaks first, followed shortly by the NTS, with the 4Vep peaking 8-9 h later.

conditions for Turing and wave instabilities in reaction-diffusion systems.

Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction-diffusion system with n components and diagonal diffusion matrix. These can be either Turing or wave instabilities. Known necessary and sufficient conditions are reproduced for there to exist diffusion rates that cause a Turing bifurcation of a stable homogeneous state in the absence of diffusion.

Modelling a dynamic magneto-agglutination bioassay.

The process of developing an end-to-end model of a magneto-immunoassay is described, simulating the agglutination effect due to the specific binding of bacteria to paramagnetic particles. After establishing the properties of the dose-specific agglutination through direct imaging, a microfluidic assay was used to demonstrate changes in the magnetophoretic transport dynamics of agglutinated clusters via transient inductive magentometer measurements. End-to-end mathematical modelling is used to establish the physical processes underlying the assay.

Getting the most out of maths: How to coordinate mathematical modelling research to support a pandemic, lessons learnt from three initiatives that were part of the COVID-19 response in the UK.

In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modelling community in the UK to be pushed to its limits.

Emergence of the London Millennium Bridge instability without synchronisation.

The pedestrian-induced instability of the London Millennium Bridge is a widely used example of Kuramoto synchronisation. Yet, reviewing observational, experimental, and modelling evidence, we argue that increased coherence of pedestrians' foot placement is a consequence of, not a cause of the instability. Instead, uncorrelated pedestrians produce positive feedback, through negative damping on average, that can initiate significant lateral bridge vibration over a wide range of natural frequencies.

Unified framework for localized patterns in reaction-diffusion systems; the Gray-Scott and Gierer-Meinhardt cases.

A recent study of canonical activator-inhibitor Schnakenberg-like models posed on an infinite line is extended to include models, such as Gray-Scott, with bistability of homogeneous equilibria. A homotopy is studied that takes a Schnakenberg-like glycolysis model to the Gray-Scott model. Numerical continuation is used to understand the complete sequence of transitions to two-parameter bifurcation diagrams within the localized pattern parameter regime as the homotopy parameter varies.

Conveyance of texture signals along a rat whisker.

Neuronal activities underlying a percept are constrained by the physics of sensory signals. In the tactile sense such constraints are frictional stick-slip events, occurring, amongst other vibrotactile features, when tactile sensors are in contact with objects. We reveal new biomechanical phenomena about the transmission of these microNewton forces at the tip of a rat's whisker, where they occur, to the base where they engage primary afferents.

The benefits of peer transparency in safe workplace operation post pandemic lockdown.

The benefits of different levels of engagement with test, trace and isolate procedures are investigated for a pandemic in which there is little population immunity, in terms of productivity and public health. Simple mathematical modelling is used in the context of a single, relatively closed workplace such as a factory or back-office where, in normal operation, each worker has lengthy interactions with a fixed set of colleagues. A discrete-time SEIR model on a fixed interaction graph is simulated with parameters that are motivated by the recent COVID-19 pandemic in the UK during a post-peak phase, including a small risk of viral infection from outside the working environment.

Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis.

The dynamics associated with bouncing-type partial contact cycles are considered for a 2 degree-of-freedom unbalanced rotor in the rigid-stator limit. Specifically, analytical explanation is provided for a previously proposed criterion for the onset upon increasing the rotor speed of single-bounce-per-period periodic motion, namely internal resonance between forward and backward whirling modes. Focusing on the cases of 2 : 1 and 3 : 2 resonances, detailed numerical results for small rotor damping reveal that stable bouncing periodic orbits, which coexist with non-contacting motion, arise just beyond the resonance speed .

Use of machine learning to analyse routinely collected intensive care unit data: a systematic review.

Background: Intensive care units (ICUs) face financial, bed management, and staffing constraints. Detailed data covering all aspects of patients' journeys into and through intensive care are now collected and stored in electronic health records: machine learning has been used to analyse such data in order to provide decision support to clinicians.

Methods: Systematic review of the applications of machine learning to routinely collected ICU data.

Tropical tree cover in a heterogeneous environment: A reaction-diffusion model.

Observed bimodal tree cover distributions at particular environmental conditions and theoretical models indicate that some areas in the tropics can be in either of the alternative stable vegetation states forest or savanna. However, when including spatial interaction in nonspatial differential equation models of a bistable quantity, only the state with the lowest potential energy remains stable. Our recent reaction-diffusion model of Amazonian tree cover confirmed this and was able to reproduce the observed spatial distribution of forest versus savanna satisfactorily when forced by heterogeneous environmental and anthropogenic variables, even though bistability was underestimated.

Towards a decision support tool for intensive care discharge: machine learning algorithm development using electronic healthcare data from MIMIC-III and Bristol, UK.

Objective: The primary objective is to develop an automated method for detecting patients that are ready for discharge from intensive care.

Design: We used two datasets of routinely collected patient data to test and improve on a set of previously proposed discharge criteria.

Setting: Bristol Royal Infirmary general intensive care unit (GICU).

Revealing instabilities in a generalized triadic supply network: A bifurcation analysis.

Supply networks are exposed to instabilities and thus a high level of risk. To mitigate this risk, it is necessary to understand how instabilities are formed in supply networks. In this paper, we focus on instabilities in inventory dynamics that develop due to the topology of the supply network.

Author Correction: Amazonian forest-savanna bistability and human impact.

This corrects the article DOI: 10.1038/ncomms15519.

Emergent acoustic order in arrays of mosquitoes.

The yellow fever mosquito Aedes aegypti forms aerial swarms that serve as mating aggregations [1]. Despite lacking the remarkable collective order of other animal ensembles, such as fish and birds [2], the kinematic properties of these swarms bear the hallmarks of local interaction and global cohesion [3,4]. However, the mechanisms responsible for collective behaviour in mosquitoes are not well understood.

Amazonian forest-savanna bistability and human impact.

A bimodal distribution of tropical tree cover at intermediate precipitation levels has been presented as evidence of fire-induced bistability. Here we subdivide satellite vegetation data into those from human-unaffected areas and those from regions close to human-cultivated zones. Bimodality is found to be almost absent in the unaffected regions, whereas it is significantly enhanced close to cultivated zones.

Quantitative analysis of harmonic convergence in mosquito auditory interactions.

This article analyses the hearing and behaviour of mosquitoes in the context of inter-individual acoustic interactions. The acoustic interactions of tethered live pairs of Aedes aegypti mosquitoes, from same and opposite sex mosquitoes of the species, are recorded on independent and unique audio channels, together with the response of tethered individual mosquitoes to playbacks of pre-recorded flight tones of lone or paired individuals. A time-dependent representation of each mosquito's non-stationary wing beat frequency signature is constructed, based on Hilbert spectral analysis.

Respiratory modulated sympathetic activity: a putative mechanism for developing vascular resistance?

Key Points: Sympathetic activity exhibits respiratory modulation that is amplified in hypertensive rats. Respiratory modulated sympathetic activity produces greater changes in vascular resistance than tonic stimulation of the same stimulus magnitude in normotensive but not hypertensive rats. Mathematical modelling demonstrates that respiratory modulated sympathetic activity may fail to produce greater vascular resistance changes in hypertensive rats because the system is saturated as a consequence of a dysfunctional noradrenaline reuptake mechanism.

The use of normal forms for analysing nonlinear mechanical vibrations.

A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recalled.

Modelling the vascular response to sympathetic postganglionic nerve activity.

This paper explores the influence of burst properties of the sympathetic nervous system on arterial contractility. Specifically, a mathematical model is constructed of the pathway from action potential generation in a sympathetic postganglionic neurone to contraction of an arterial smooth muscle cell. The differential equation model is a synthesis of models of the individual physiological processes, and is shown to be consistent with physiological data.

Time-frequency composition of mosquito flight tones obtained using Hilbert spectral analysis.

Techniques for estimating temporal variation in the frequency content of acoustic tones based on short-time fast Fourier transforms are fundamentally limited by an inherent time-frequency trade-off. This paper presents an alternative methodology, based on Hilbert spectral analysis, which is not affected by this weakness, and applies it to the accurate estimation of mosquito wing beat frequencies. Mosquitoes are known to communicate with one another via the sounds generated by their flapping wings.

Subcritical Turing bifurcation and the morphogenesis of localized patterns.

Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localized patterns via the homoclinic snaking mechanism. This phenomenon is shown to occur naturally when balancing source and loss effects are included in a typical reaction-diffusion system, leading to a super- to subcritical transition. Implications are discussed [corrected]for a range of physical problems, arguing that subcriticality leads to naturally robust phase transitions to localized patterns.