scholarly journals Spread of competing viruses on heterogeneous networks

2017 ◽  
Vol 375 (2096) ◽  
pp. 20160284 ◽  
Author(s):  
Shanshan Chen ◽  
Kaihua Wang ◽  
Mengfeng Sun ◽  
Xinchu Fu
Keyword(s):  
Heterogeneous Networks ◽  
Reproduction Number ◽  
Mean Field ◽  
Probability Generating Function ◽  
Sir Model ◽  
Dynamical Behaviour ◽  
Theoretical Research ◽  
Mathematical Methods ◽  
Field Approach ◽  
Spreading Dynamics

In this paper, we propose a model where two strains compete with each other at the expense of common susceptible individuals on heterogeneous networks by using pair-wise approximation closed by the probability-generating function (PGF). All of the strains obey the susceptible–infected–recovered (SIR) mechanism. From a special perspective, we first study the dynamical behaviour of an SIR model closed by the PGF, and obtain the basic reproduction number via two methods. Then we build a model to study the spreading dynamics of competing viruses and discuss the conditions for the local stability of equilibria, which is different from the condition obtained by using the heterogeneous mean-field approach. Finally, we perform numerical simulations on Barabási–Albert networks to complement our theoretical research, and show some dynamical properties of the model with competing viruses. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.

Spreading of Epidemics on Scale-Free Networks with Time Delay

2012 ◽  
Vol 562-564 ◽  
pp. 1386-1389
Author(s):  
Yuan Mei Wang ◽  
Tao Li
Keyword(s):  
Field Theory ◽  
Time Delay ◽  
Mean Field Theory ◽  
Mean Field ◽  
Sir Model ◽  
Scale Free ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
The Mean ◽  
Theoretical Results

In the SIR model once a node is cured after infection it becomes permanently immune,but we assume this immunity to be temporary. So we obtain an epidemic model with time delay on scale-free networks. Using the mean field theory the spreading threshold and the spreading dynamics is analyzed. Theoretical results indicate that the threshold is significantly dependent on the topology of scale-free networks and time delay. Numerical simulations confirmed the theoretical results.

Epidemic spreading of interacting diseases with activity of nodes reshapes the critical threshold

2017 ◽  
Vol 28 (01) ◽  
pp. 1750013 ◽  
Author(s):  
Chongjun Fan ◽  
Yang Jin ◽  
Liang-An Huo ◽  
Chen Liu ◽  
Yunpeng Yang
Keyword(s):  
Temporal Evolution ◽  
Mean Field ◽  
Critical Threshold ◽  
Epidemic Spreading ◽  
Final Size ◽  
Node Activity ◽  
Transmission Rates ◽  
Field Approach ◽  
Spreading Dynamics ◽  
Theoretical Predictions

In this paper, based on susceptible–infected–susceptible (SIS) scheme, we introduce a framework that allows us to describe the spreading dynamics of two interacting diseases with active nodes. Different from previous studies, the two different diseases, propagating concurrently on the same population, can interact with each other by modifying their transmission rates. Meanwhile, according to certain probabilities, each node on the complex networks rotates between active state and inactive state. Based on heterogeneous mean-field approach, we analyze the epidemic thresholds of the two diseases and compute the temporal evolution characterizing the spreading dynamics. In addition, we validate these theoretical predictions by numerical simulations with phase diagrams. Results show that the secondary thresholds for the two opposite scenarios (mutual enhancement scenario and mutual impairment scenario) are different. We also find that the value of critical threshold and the final size of spreading dynamics are reduced as the node activity rate decreases.

scholarly journals Inhomogeneous mean-field approach to collective excitations near the superfluid-Mott glass transition

2021 ◽  
pp. 168526
Author(s):  
Martin Puschmann ◽  
João C. Getelina ◽  
José A. Hoyos ◽  
Thomas Vojta
Keyword(s):  
Glass Transition ◽  
Mean Field ◽  
Collective Excitations ◽  
Field Approach

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

scholarly journals Effect of Bjerrum pairs on electrostatic properties in an electrolyte solution near charged surfaces: A mean-field approach

2021 ◽  
Author(s):  
Jun-Sik Sin
Keyword(s):  
Electrolyte Solution ◽  
Size Effects ◽  
Mean Field ◽  
Finite Size ◽  
Ion Association ◽  
Finite Size Effects ◽  
Field Approach ◽  
Electrostatic Properties ◽  
Charged Surfaces ◽  
Orientational Ordering

In this paper, we investigate the consequences of ion association, coupled with the considerations of finite size effects and orientational ordering of Bjerrum pairs as well as ions and water...

scholarly journals Electron liquid state in the symmetric Anderson lattice

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Igor N. Karnaukhov
Keyword(s):  
Low Temperatures ◽  
Arbitrary Dimension ◽  
Mean Field ◽  
Coulomb Repulsion ◽  
Anomalous Behavior ◽  
Effective Field ◽  
Kondo Lattice ◽  
Field Approach ◽  
Cubic Lattices ◽  
Half Filling

AbstractUsing mean field approach, we provide analytical and numerical solution of the symmetric Anderson lattice for arbitrary dimension at half filling. The symmetric Anderson lattice is equivalent to the Kondo lattice, which makes it possible to study the behavior of an electron liquid in the Kondo lattice. We have shown that, due to hybridization (through an effective field due to localized electrons) of electrons with different spins and momenta $$\mathbf{k} $$ k and $$\mathbf{k} +\overrightarrow{\pi }$$ k + π → , the gap in the electron spectrum opens at half filling. Such hybridization breaks the conservation of the total magnetic momentum of electrons, the spontaneous symmetry is broken. The state of electron liquid is characterized by a large Fermi surface. A gap in the spectrum is calculated depending on the magnitude of the on-site Coulomb repulsion and value of s–d hybridization for the chain, as well as for square and cubic lattices. Anomalous behavior of the heat capacity at low temperatures in the gapped state, which is realized in the symmetric Anderson lattice, was also found.

scholarly journals Quantal description of nucleon exchange in a stochastic mean-field approach

2015 ◽  
Vol 91 (5) ◽  
Author(s):  
S. Ayik ◽  
O. Yilmaz ◽  
B. Yilmaz ◽  
A. S. Umar ◽  
A. Gokalp ◽  
...  
Keyword(s):  
Mean Field ◽  
Field Approach

Characterization of Textured Aluminum Lines and Modelling of Stress Voiding

1994 ◽  
Vol 343 ◽  
Author(s):  
S.C. Wardle ◽  
B.L. Adams ◽  
C.S. Nichols ◽  
D.A. Smith
Keyword(s):  
Free Energy ◽  
Excess Free Energy ◽  
Mean Field ◽  
High Energy ◽  
Polycrystalline Structure ◽  
Field Approach ◽  
Bamboo Structure ◽  
Automated Technique ◽  
Theory And Modeling

ABSTRACTIt is well known from studies of individual interfaces that grain boundaries exhibit a spectrum of properties because their structure is misorientation dependent. Usually this variability is neglected and properties are modeled using a mean field approach. The limitations inherent in this approach can be overcome, in principle, using a combination of experimental techniques, theory and modeling. The bamboo structure of an interconnect is a particularly simple polycrystalline structure that can now be readily characterized experimentally and modeled in the computer. The grain misorientations in a [111] textured aluminum line have been measured using the new automated technique of orientational imaging microscopy. By relating boundary angle to diffusivity the expected stress voiding failure processes can be predicted through the link between misorientation angle, grain boundary excess free energy and diffusivity. Consequently it can be shown that the high energy boundaries are the favored failure sites thermodynamically and kinetically.

THE INNER CRUST OF NEUTRON STARS IN RELATIVISTIC MEAN FIELD APPROACH

2008 ◽  
Vol 17 (09) ◽  
pp. 1765-1773 ◽  
Author(s):  
JIGUANG CAO ◽  
ZHONGYU MA ◽  
NGUYEN VAN GIAI
Keyword(s):  
Boundary Conditions ◽  
Neutron Stars ◽  
Mean Field ◽  
Bcs Theory ◽  
Neutron Density ◽  
Field Approach ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Density Distributions ◽  
Rmf Model

The microscopic properties and superfluidity of the inner crust in neutron stars are investigated in the framework of the relativistic mean field(RMF) model and BCS theory. The Wigner-Seitz(W-S) cell of inner crust is composed of neutron-rich nuclei immersed in a sea of dilute, homogeneous neutron gas. The pairing properties of nucleons in the W-S cells are treated in BCS theory with Gogny interaction. In this work, we emphasize on the choice of the boundary conditions in the RMF approach and superfluidity of the inner crust. Three kinds of boundary conditions are suggested. The properties of the W-S cells with the three kinds of boundary conditions are investigated. The neutron density distributions in the RMF and Hartree-Fock-Bogoliubov(HFB) models are compared.

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