scholarly journals An overview of epidemic models with phase transitions to absorbing states running on top of complex networks

2021 ◽  
Vol 31 (1) ◽  
pp. 012101
Author(s):  
Angélica S. Mata
Keyword(s):  
Phase Transitions ◽  
Complex Networks ◽  
Epidemic Models ◽  
Absorbing States

scholarly journals Phase transitions with infinitely many absorbing states in complex networks

2013 ◽  
Vol 87 (2) ◽  
Author(s):  
Renan S. Sander ◽  
Silvio C. Ferreira ◽  
Romualdo Pastor-Satorras
Keyword(s):  
Phase Transitions ◽  
Complex Networks ◽  
Absorbing States

scholarly journals The Role of Movement Patterns in Epidemic Models on Complex Networks

2021 ◽  
Vol 83 (10) ◽  
Author(s):  
Alfonso Ruiz-Herrera ◽  
Pedro J. Torres
Keyword(s):  
Complex Networks ◽  
Network Theory ◽  
Diffusion Rate ◽  
Critical Role ◽  
Movement Patterns ◽  
Epidemic Models ◽  
Simplifying Assumptions ◽  
The Common

AbstractIn this paper, we analyze the influence of the usual movement variables on the spread of an epidemic. Specifically, given two spatial topologies, we can deduce which topology produces less infected individuals. In particular, we determine the topology that minimizes the overall number of infected individuals. It is worth noting that we do not assume any of the common simplifying assumptions in network theory such as all the links have the same diffusion rate or the movement of the individuals is symmetric. Our main conclusion is that the degree of mobility of the population plays a critical role in the spread of a disease. Finally, we derive theoretical insights to management of epidemics.

scholarly journals Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks

2015 ◽  
Vol 111 (6) ◽  
pp. 60009 ◽  
Author(s):  
M. Krasnytska ◽  
B. Berche ◽  
Yu. Holovatch ◽  
R. Kenna
Keyword(s):  
Phase Transitions ◽  
Complex Networks ◽  
Circle Theorem

Mathematical models for phase transitions in biogels

2019 ◽  
Vol 33 (09) ◽  
pp. 1950111 ◽  
Author(s):  
Ayse Humeyra Bilge ◽  
Arif Selcuk Ogrenci ◽  
Onder Pekcan
Keyword(s):  
Phase Transitions ◽  
Critical Point ◽  
Transition Point ◽  
Extreme Values ◽  
Sol Gel ◽  
Epidemic Models ◽  
Gel Point ◽  
Sis Model ◽  
First Derivative ◽  
Sir Epidemic

It has been shown that reversible and irreversible phase transitions of biogels can be represented by epidemic models. The irreversible chemical sol–gel transitions are modeled by the Susceptible-Exposed-Infected-Removed (SEIR) or Susceptible-Infected-Removed (SIR) epidemic systems whereas reversible physical gels are modeled by a modification of the Susceptible-Infected-Susceptible (SIS) system. Measured sol–gel and gel–sol transition data have been fitted to the solutions of the epidemic models, either by solving the differential equations directly (SIR and SEIR models) or by nonlinear regression (SIS model). The gel point is represented as the “critical point of sigmoid,” defined as the limit point of the locations of the extreme values of its derivatives. Then, the parameters of the sigmoidal curve representing the gelation process are used to predict the gel point and its relative position with respect to the transition point, that is, the maximum of the first derivative with respect to time. For chemical gels, the gel point is always located before the maximum of the first derivative and moves backward in time as the strength of the activation increases. For physical gels, the critical point for the sol–gel transition occurs before the maximum of the first derivative with respect to time, that is, it is located at the right of this maximum with respect to temperature. For gel–sol transitions, the critical point is close to the transition point; the critical point occurs after the maximum of the first derivative for low concentrations whereas the critical point occurs after the maximum of the first derivative for higher concentrations.

scholarly journals PHASE TRANSITIONS IN SOME EPIDEMIC MODELS DEFINED ON SMALL-WORLD NETWORKS

2003 ◽  
Vol 14 (06) ◽  
pp. 825-833 ◽  
Author(s):  
H. N. AGIZA ◽  
A. S. ELGAZZAR ◽  
S. A. YOUSSEF
Keyword(s):  
Phase Transitions ◽  
Small World ◽  
Epidemic Models ◽  
Small World Networks ◽  
Inhomogeneous Models ◽  
Sirs Model ◽  
Variable Susceptibility

Some modified versions of susceptible-infected-recovered-susceptible (SIRS) model are defined on small-world networks. Latency, incubation and variable susceptibility are separately included. Phase transitions in these models are studied. Then inhomogeneous models are introduced. In some cases, the application of the models to small-world networks is shown to increase the epidemic region.

Application of epidemic models to phase transitions

2012 ◽  
Vol 85 (11) ◽  
pp. 1009-1017 ◽  
Author(s):  
A.H. Bilge ◽  
Ö. Pekcan ◽  
M.V. Gürol
Keyword(s):  
Phase Transitions ◽  
Epidemic Models
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