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.

Research on SIQRS Spreading Dynamic Model with Feedback Mechanism on Scale-Free Networks

2014 ◽  
Vol 989-994 ◽  
pp. 4524-4527
Author(s):  
Tao Li ◽  
Yuan Mei Wang ◽  
You Ping Yang
Keyword(s):  
Dynamic Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Feedback Mechanism ◽  
Epidemic Spreading ◽  
Scale Free ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
The Mean ◽  
The Relationship

A modified spreading dynamic model with feedback-mechanism based on scale-free networks is presented in this study. Using the mean field theory, the spreading dynamics of the model is analyzed. The spreading threshold and equilibriums are derived. The relationship between the spreading threshold, the epidemic steady-state and the feedback-mechanism is analyzed in detail. Theoretical results indicate the feedback-mechanism can increase the spreading threshold, resulting in effectively controlling the epidemic spreading.

Spreading Dynamics Analysis of a Novel SEAIRS Epidemic Model with Protection and Hospital Quarantine under Government Pre-warning

2021 ◽  
Author(s):  
Bingchuan Xue ◽  
Tao Li ◽  
Xinming Cheng ◽  
Yumiao Li ◽  
Yuanyuan Wu ◽  
...  
Keyword(s):  
Epidemic Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Epidemic Spreading ◽  
Scale Free ◽  
Spreading Dynamics ◽  
The Mean ◽  
The Impact

Abstract To study the impact of protection and hospital quarantine measure, government pre-warning mechanism and heterogeneity of underlying networks on epidemic spreading, a novel SEAIRS epidemic model is proposed on scale-free networks. The spreading dynamics of the model is studied by means of the mean-field theory. Two equilibriums and the basic reproductive number R0 of the model is analyzed in detail. The global asymptotic stability of the disease-free equilibrium, the permanence of the epidemic spreading and the global attractivity of the endemic equilibrium are proved. Sensitivity analysis shows that the basic reproductive number R0 is dependent on the coverage rate of home quarantine (ωQ,ηA ,ηS ), hospitalization rate η1 and government pre-warning intensity δ . Finally, the theoretical analysis results are confirmed by means of numerical simulations.

Epidemic Spreading with Feedback Mechanism and Time Delay under Migration in Scale-Free Networks

2013 ◽  
Vol 378 ◽  
pp. 655-661
Author(s):  
Tao Li ◽  
Yuan Mei Wang
Keyword(s):  
Time Delay ◽  
Mean Field Theory ◽  
Mean Field ◽  
Feedback Mechanism ◽  
Critical Threshold ◽  
Epidemic Spreading ◽  
Scale Free ◽  
Epidemic Dynamics ◽  
Scale Free Networks ◽  
The Mean

Taking into account the heterogeneity of the underlying networks, an epidemic model with feedback-mechanism, time delay and migrations of individuals on scale-free networks is presented. First, the epidemic dynamics is analyzed via the mean field theory. The spreading critical threshold and equilibriums are derived. The existence of endemic equilibrium is determined by the spreading threshold. Then, the influences of feedback-mechanism, time delay, migrations of individuals and the heterogeneity of the scale-free networks on the spreading threshold and the epidemic steady-state are studied in detail. Numerical simulations are presented to illustrate the results with the theoretical analysis.

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’.

scholarly journals Nonperturbative heterogeneous mean-field approach to epidemic spreading in complex networks

2011 ◽  
Vol 84 (3) ◽  
Author(s):  
Sergio Gómez ◽  
Jesús Gómez-Gardeñes ◽  
Yamir Moreno ◽  
Alex Arenas
Keyword(s):  
Complex Networks ◽  
Mean Field ◽  
Epidemic Spreading ◽  
Field Approach

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 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
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