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.

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.

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 .

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.

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.

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.

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.

Increased intrinsic excitability of muscle vasoconstrictor preganglionic neurons may contribute to the elevated sympathetic activity in hypertensive rats.

Hypertension is associated with pathologically increased sympathetic drive to the vasculature. This has been attributed to increased excitatory drive to sympathetic preganglionic neurons (SPN) from brainstem cardiovascular control centers. However, there is also evidence supporting increased intrinsic excitability of SPN.

The impacting cantilever: modal non-convergence and the importance of stiffness matching.

The problem of an Euler-Bernoulli cantilever beam whose free end impacts with a point constraint is revisited from the point of view of modal analysis. It is shown that there is non-uniqueness of consistent impact laws for a given modal truncation. Moreover, taking an N-mode compliant, bilinear formulation and passing to the rigid limit leads to a sequence of impact models that does not converge as N--> ∞.