scholarly journals Integrating stochasticity and network structure into an epidemic model

2008 ◽  
Vol 6 (38) ◽  
pp. 761-774 ◽  
Author(s):  
C. E. Dangerfield ◽  
J. V. Ross ◽  
M. J. Keeling
Keyword(s):  
Spatial Structure ◽  
Network Structure ◽  
Mean Field ◽  
Deterministic Models ◽  
Mean Field Model ◽  
Epidemic Dynamics ◽  
Infection Dynamics ◽  
Pairwise Model ◽  
The Impact ◽  
First Time

While the foundations of modern epidemiology are based upon deterministic models with homogeneous mixing, it is being increasingly realized that both spatial structure and stochasticity play major roles in shaping epidemic dynamics. The integration of these two confounding elements is generally ascertained through numerical simulation. Here, for the first time, we develop a more rigorous analytical understanding based on pairwise approximations to incorporate localized spatial structure and diffusion approximations to capture the impact of stochasticity. Our results allow us to quantify, analytically, the impact of network structure on the variability of an epidemic. Using the susceptible–infectious–susceptible framework for the infection dynamics, the pairwise stochastic model is compared with the stochastic homogeneous-mixing (mean-field) model—although to enable a fair comparison the homogeneous-mixing parameters are scaled to give agreement with the pairwise dynamics. At equilibrium, we show that the pairwise model always displays greater variation about the mean, although the differences are generally small unless the prevalence of infection is low. By contrast, during the early epidemic growth phase when the level of infection is increasing exponentially, the pairwise model generally shows less variation.

scholarly journals Building epidemiological models from R 0 : an implicit treatment of transmission in networks

2006 ◽  
Vol 274 (1609) ◽  
pp. 505-512 ◽  
Author(s):  
Juan Pablo Aparicio ◽  
Mercedes Pascual
Keyword(s):  
Network Structure ◽  
Mean Field ◽  
Basic Reproductive Number ◽  
Disease Spread ◽  
Reproductive Number ◽  
Detailed Knowledge ◽  
Deterministic Models ◽  
Mean Field Model ◽  
Contact Networks ◽  
Individual Level

Simple deterministic models are still at the core of theoretical epidemiology despite the increasing evidence for the importance of contact networks underlying transmission at the individual level. These mean-field or ‘compartmental’ models based on homogeneous mixing have made, and continue to make, important contributions to the epidemiology and the ecology of infectious diseases but fail to reproduce many of the features observed for disease spread in contact networks. In this work, we show that it is possible to incorporate the important effects of network structure on disease spread with a mean-field model derived from individual level considerations. We propose that the fundamental number known as the basic reproductive number of the disease, R 0 , which is typically derived as a threshold quantity, be used instead as a central parameter to construct the model from. We show that reliable estimates of individual level parameters can replace a detailed knowledge of network structure, which in general may be difficult to obtain. We illustrate the proposed model with small world networks and the classical example of susceptible–infected–recovered ( SIR ) epidemics.

scholarly journals Hamiltonian mean field model: Effect of network structure on synchronization dynamics

2015 ◽  
Vol 92 (5) ◽  
Author(s):  
Yogesh S. Virkar ◽  
Juan G. Restrepo ◽  
James D. Meiss
Keyword(s):  
Network Structure ◽  
Field Model ◽  
Mean Field ◽  
Mean Field Model

scholarly journals Complex dynamics of synergistic coinfections on realistically clustered networks

2015 ◽  
Vol 112 (33) ◽  
pp. 10551-10556 ◽  
Author(s):  
Laurent Hébert-Dufresne ◽  
Benjamin M. Althouse
Keyword(s):  
Contact Structure ◽  
Complex Dynamics ◽  
Mean Field ◽  
Epidemiological Data ◽  
Single Individual ◽  
Mean Field Model ◽  
Speed Up ◽  
First Order Transition ◽  
Clustered Networks ◽  
The Impact

We investigate the impact of contact structure clustering on the dynamics of multiple diseases interacting through coinfection of a single individual, two problems typically studied independently. We highlight how clustering, which is well known to hinder propagation of diseases, can actually speed up epidemic propagation in the context of synergistic coinfections if the strength of the coupling matches that of the clustering. We also show that such dynamics lead to a first-order transition in endemic states, where small changes in transmissibility of the diseases can lead to explosive outbreaks and regions where these explosive outbreaks can only happen on clustered networks. We develop a mean-field model of coinfection of two diseases following susceptible-infectious-susceptible dynamics, which is allowed to interact on a general class of modular networks. We also introduce a criterion based on tertiary infections that yields precise analytical estimates of when clustering will lead to faster propagation than nonclustered networks. Our results carry importance for epidemiology, mathematical modeling, and the propagation of interacting phenomena in general. We make a call for more detailed epidemiological data of interacting coinfections.

On the Vanishing of Spherical Shell Gap at N = 28 in 44S Using Relativistic Mean-Field Model

1997 ◽  
Vol 12 (18) ◽  
pp. 1317-1325 ◽  
Author(s):  
Raj K. Gupta ◽  
S. K. Patra ◽  
W. Greiner
Keyword(s):  
Spherical Shell ◽  
Ground State ◽  
Field Model ◽  
Mean Field ◽  
Light Nuclei ◽  
Shape Coexistence ◽  
Mean Field Model ◽  
Relativistic Mean Field ◽  
Pairing Strength ◽  
First Time

Use of the NL-SH parameter set is re-analyzed and a new parameter set TM2 is used for the first time in the axially deformed self-consistent relativistic mean-field calculations for 44 S and its neighboring nuclei 40 Mg and 42 Si . The spherical shell gap at N=28 in 44 S is found to be intact for the TM2 parameter set since it predicts the ground state of 44 S as nearly spherical, irrespective of the strength of the pairing force. The predictions of the NL-SH parameter set for 44 S are found to depend strongly on the pairing strength and, due to shape coexistence, the ground state could be strongly prolate or strongly oblate deformed. Hence, for the NL-SH parameter set, the spherical shell gap at N=28 in 44 S is broken for either of the prolate/oblate deformation. For 40 Mg and 42 Si , the spherical shell gap at N=28 is found broken under all conditions since the predicted deformations are large, independent of both the pairing strength and the choice of parameter set. This calls for immediate measurements of the deformations of these nuclei, particularly for 44 S which will decide its shell structure as well as the region of deformation in light nuclei.

scholarly journals Small-scale spatial structure influences large-scale invasion rates

2019 ◽  
Author(s):  
Michael J. Plank ◽  
Matthew J. Simpson ◽  
Rachelle N. Binny
Keyword(s):  
Population Dynamics ◽  
Spatial Structure ◽  
Large Scale ◽  
Spatial Scales ◽  
Mean Field ◽  
Average Density ◽  
Small Scale ◽  
Local Interactions ◽  
Mean Field Model ◽  
Species Invasions

AbstractLocal interactions among individual members of a population can generate intricate small-scale spatial structure, which can strongly influence population dynamics. The two-way interplay between local interactions and population dynamics is well understood in the relatively simple case where the population occupies a fixed domain with a uniform average density. However, the situation where the average population density is spatially varying is less well understood. This situation includes ecologically important scenarios such as species invasions, range shifts, and moving population fronts. Here, we investigate the dynamics of the spatial stochastic logistic model in a scenario where an initially confined population subsequently invades new, previously unoccupied territory. This simple model combines density-independent proliferation with dispersal, and density-dependent mortality via competition with other members of the population. We show that, depending on the spatial scales of dispersal and competition, either a clustered or a regular spatial structure develops over time within the invading population. In the short-range dispersal case, the invasion speed is significantly lower than standard predictions of the mean-field model. We conclude that mean-field models, even when they account for non-local processes such as dispersal and competition, can give misleading predictions for the speed of a moving invasion front.

scholarly journals From synaptic activity to human in vivo quantification of neurotransmitter dynamics: a neural modelling approach

2021 ◽  
Author(s):  
Caroline A. Lea-Carnall ◽  
Wael El-Deredy ◽  
Stephen R. Williams ◽  
Charlotte J. Stagg ◽  
Nelson J. Trujillo-Barreto
Keyword(s):  
Mean Field ◽  
Neural Dynamics ◽  
Resonance Spectroscopy ◽  
Mean Field Model ◽  
Physiological Basis ◽  
1H Magnetic Resonance Spectroscopy ◽  
Dependent Change ◽  
First Time ◽  
Activity Dependent

AbstractUnderstanding the role of neurotransmitters glutamate and GABA during normal and abnormal brain function and under external stimulation in humans are critical neuroscientific and clinical goals. The recent development of functional 1H-Magnetic resonance spectroscopy (fMRS) has allowed us to study neuro-transmitter activity in vivo for the first time. However, the physiological basis of the observed fMRS signal remains unclear. It has been proposed that fMRS detects shifts in metabolite concentrations as they move from presynaptic vesicles, where they are largely invisible, to extracellular and cytosolic pools, where they are visible.Here we bridge the gap between neural dynamics and fMRS by developing a mean-field model to link the neurotransmitter dynamics at the microscopic-level to the macroscopic-level imaging measurements. GABA and glutamate are described as cycling between three metabolic pools: in the vesicles; active in the cleft; or undergoing recycling in the astrocytic or neuronal cytosol. We interrogate the model by applying a current to manipulate the mean membrane potential and firing rate of the neural populations.We find that by disregarding the contribution from the vesicular pool, our model predicts activity-dependent changes in the MRS signal, which are consistent with reported empirical findings. Further, we show that current magnitude and direction has a selective effect on the GABA/glutamate-MRS signal: inhibitory stimulation leads to reduction of both metabolites, whereas excitatory stimulation leads to increased glutamate and decreased GABA. In doing so, we link neural dynamics and fMRS and provide a mechanistic account for the activity-dependent change in the observed MRS signal.Key Points SummaryThe recent development of functional 1H-Magnetic resonance spectroscopy (fMRS) has allowed us to study neurotransmitter activity in vivo for the first time in humans. However, the physiological basis of the observed fMRS signal is unclear.It has been proposed that fMRS detects shifts in metabolite concentrations as they move from presynaptic vesicles, where they are largely invisible to MRS, to extracellular and cytosolic pools, where they are visible to MRS.We test this hypothesis using a mean field model which links the neural dynamics of neurotransmitters at the microscopic-level to the macroscopic-level imaging measurements obtained in experimental studies.By disregarding activity in the vesicular pool, our model can generate activity-dependent changes in the MRS signal in response to stimulation which are consistent with experimental findings in the literature.We provide a mechanistic account for the activity-dependent change in observed neurotransmitter concentrations using MRS.

scholarly journals Hyperons and quarks in proto-neutron stars

2019 ◽  
Vol 486 (4) ◽  
pp. 5441-5447 ◽  
Author(s):  
J Roark ◽  
X Du ◽  
C Constantinou ◽  
V Dexheimer ◽  
A W Steiner ◽  
...  
Keyword(s):  
Neutron Stars ◽  
Finite Temperature ◽  
Degrees Of Freedom ◽  
Mean Field ◽  
Large Mass ◽  
Stellar Structure ◽  
Stellar Rotation ◽  
Mean Field Model ◽  
Relativistic Mean Field ◽  
The Impact

ABSTRACT In this work, we study matter in the cores of proto-neutron stars, focusing on the impact of their composition on the stellar structure. We begin by examining the effects of finite temperature (through a fixed entropy per baryon) and lepton fraction on purely nucleonic matter by making use of the DSH (Du, Steiner & Holt) model. We then turn our attention to a relativistic mean-field model containing exotic degrees of freedom, the Chiral Mean Field (CMF) model, again, under the conditions of finite temperature and trapped neutrinos. In the latter, since both hyperons and quarks are found in the cores of large-mass stars, their interplay and the possibility of mixtures of phases is taken into account and analysed. Finally, we discuss how stellar rotation can affect our results.

scholarly journals Poisson-distributed noise induces cortical γ-activity: explanation of γ-enhancement by anaesthetics ketamine and propofol

2021 ◽  
Author(s):  
Thomas Martin Wahl ◽  
Axel Hutt
Keyword(s):  
Coherent State ◽  
Analytical Study ◽  
Additive Noise ◽  
Resonance Effect ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Frequency Range ◽  
Noise Levels ◽  
Mean Field Model ◽  
The Impact

Abstract Additive noise is known to affect the stability of nonlinear systems. To understand better the role of additive noise in neural systems, we investigate the impact of additive noise on a random neural network of excitatory and inhibitory neurons. Here we hypothesize that the noise originates from the ascending reticular activating system (ARAS). Coherence resonance in the γ-frequency range emerges for intermediate noise levels while the network exhibits non-coherent activity at low and high noise levels. The analytical study of a corresponding mean-field model system explains the resonance effect by a noise-induced phase transition via a saddle-node bifurcation. An analytical study of the linear mean-field systems response to additive noise reveals that the coherent state exhibits a quasi-cycle in the γ-frequency range whose spectral properties are tuned by the additive noise. To illustrate the importance of the work, we show that the quasi-cycle explains γ-enhancement under impact of the anaesthetics ketamine and propofol as a destabilizing effect of the coherent state.

scholarly journals Modelling digital and manual contact tracing for COVID-19. Are low uptakes and missed contacts deal-breakers?

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0259969
Author(s):  
Andrei C. Rusu ◽  
Rémi Emonet ◽  
Katayoun Farrahi
Keyword(s):  
Field Model ◽  
Mean Field ◽  
Health Interventions ◽  
Contact Tracing ◽  
Public Health Interventions ◽  
Mean Field Model ◽  
Pathogen Dynamics ◽  
Usage Patterns ◽  
The Right ◽  
The Impact

Comprehensive testing schemes, followed by adequate contact tracing and isolation, represent the best public health interventions we can employ to reduce the impact of an ongoing epidemic when no or limited vaccine supplies are available and the implications of a full lockdown are to be avoided. However, the process of tracing can prove feckless for highly-contagious viruses such as SARS-CoV-2. The interview-based approaches often miss contacts and involve significant delays, while digital solutions can suffer from insufficient adoption rates or inadequate usage patterns. Here we present a novel way of modelling different contact tracing strategies, using a generalized multi-site mean-field model, which can naturally assess the impact of manual and digital approaches alike. Our methodology can readily be applied to any compartmental formulation, thus enabling the study of more complex pathogen dynamics. We use this technique to simulate a newly-defined epidemiological model, SEIR-T, and show that, given the right conditions, tracing in a COVID-19 epidemic can be effective even when digital uptakes are sub-optimal or interviewers miss a fair proportion of the contacts.

scholarly journals Hamiltonian mean-field model: effect of temporal perturbation in coupling matrix

2018 ◽  
Vol 32 (14) ◽  
pp. 1850147 ◽  
Author(s):  
Nivedita Bhadra ◽  
Soumen K. Patra
Keyword(s):  
Critical Point ◽  
Numerical Study ◽  
Coupling Parameter ◽  
Modulation Frequency ◽  
Mean Field ◽  
Critical Energy ◽  
Temporal Modulation ◽  
Coupling Matrix ◽  
Mean Field Model ◽  
The Impact

The Hamiltonian mean-field (HMF) model is a system of fully coupled rotators which exhibits a second-order phase transition at some critical energy in its canonical ensemble. We investigate the case where the interaction between the rotors is governed by a time-dependent coupling matrix. Our numerical study reveals a shift in the critical point due to the temporal modulation. The shift in the critical point is shown to be independent of the modulation frequency above some threshold value, whereas the impact of the amplitude of modulation is dominant. In the microcanonical ensemble, the system with constant coupling reaches a quasi-stationary state (QSS) at an energy near the critical point. Our result indicates that the QSS subsists in presence of such temporal modulation of the coupling parameter.

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