scholarly journals Protection Strategy for Edge-Weighted Graphs in Disease Spread

2021 ◽  
Vol 11 (11) ◽  
pp. 5115
Author(s):  
Ronald Manríquez ◽  
Camilo Guerrero-Nancuante ◽  
Carla Taramasco
Keyword(s):  
Infectious Disease ◽  
Weighted Graph ◽  
Sir Model ◽  
Disease Spread ◽  
Weighted Graphs ◽  
Fake News ◽  
Scale Free ◽  
Protection Strategy ◽  
Immunization Strategies ◽  
Scale Free Networks

Fake news, viruses on computer systems or infectious diseases on communities are some of the problems that are addressed by researchers dedicated to study complex networks. The immunization process is the solution to these challenges and hence the importance of obtaining immunization strategies that control these spreads. In this paper, we evaluate the effectiveness of the DIL-Wα ranking in the immunization of nodes that are attacked by an infectious disease that spreads on an edge-weighted graph using a graph-based SIR model. The experimentation was done on real and scale-free networks and the results illustrate the benefits of this ranking.

scholarly journals Spread of Epidemic Disease on Edge-Weighted Graphs from a Database: A Case Study of COVID-19

2021 ◽  
Vol 18 (9) ◽  
pp. 4432
Author(s):  
Ronald Manríquez ◽  
Camilo Guerrero-Nancuante ◽  
Felipe Martínez ◽  
Carla Taramasco
Keyword(s):  
Public Health ◽  
Infectious Diseases ◽  
Preventive Measures ◽  
Weighted Graph ◽  
Real Data ◽  
Sir Model ◽  
Weighted Graphs ◽  
Epidemic Disease ◽  
The Real

The understanding of infectious diseases is a priority in the field of public health. This has generated the inclusion of several disciplines and tools that allow for analyzing the dissemination of infectious diseases. The aim of this manuscript is to model the spreading of a disease in a population that is registered in a database. From this database, we obtain an edge-weighted graph. The spreading was modeled with the classic SIR model. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics. Moreover, a deterministic approximation is provided. With database COVID-19 from a city in Chile, we analyzed our model with relationship variables between people. We obtained a graph with 3866 vertices and 6,841,470 edges. We fitted the curve of the real data and we have done some simulations on the obtained graph. Our model is adjusted to the spread of the disease. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics, in this case with real data of COVID-19. This valuable information allows us to also include/understand the networks of dissemination of epidemics diseases as well as the implementation of preventive measures of public health. These findings are important in COVID-19’s pandemic context.

scholarly journals Network rewiring dynamics with convergence towards a star network

2016 ◽  
Vol 472 (2194) ◽  
pp. 20160236 ◽  
Author(s):  
P. A. Whigham ◽  
G. Dick ◽  
M. Parry
Keyword(s):  
Infectious Disease ◽  
Random Network ◽  
Small World ◽  
Fixation Time ◽  
Fixed Size ◽  
Star Network ◽  
Scale Free ◽  
Link Type ◽  
Scale Free Networks ◽  
Network Rewiring

Network rewiring as a method for producing a range of structures was first introduced in 1998 by Watts & Strogatz ( Nature 393 , 440–442. ( doi:10.1038/30918 )). This approach allowed a transition from regular through small-world to a random network. The subsequent interest in scale-free networks motivated a number of methods for developing rewiring approaches that converged to scale-free networks. This paper presents a rewiring algorithm (RtoS) for undirected, non-degenerate, fixed size networks that transitions from regular, through small-world and scale-free to star-like networks. Applications of the approach to models for the spread of infectious disease and fixation time for a simple genetics model are used to demonstrate the efficacy and application of the approach.

scholarly journals EFFECTS OF AGING AND LINKS REMOVAL ON EPIDEMIC DYNAMICS IN SCALE-FREE NETWORKS

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2534-2539 ◽  
Author(s):  
K. P. CHAN ◽  
DAFANG ZHENG ◽  
P. M. HUI
Keyword(s):  
Preferential Attachment ◽  
Aging Effect ◽  
Sir Model ◽  
Scale Free ◽  
Epidemic Dynamics ◽  
Local Spread ◽  
Scale Free Networks ◽  
Effects Of Aging ◽  
Growing Network ◽  
Aging Factor

We study the combined effects of aging and links removal on epidemic dynamics in the Barabási–Albert scale-free networks. The epidemic is described by a susceptible-infected-refractory (SIR) model. The aging effect of a node introduced at time ti is described by an aging factor of the form (t-ti)-β in the probability of being connected to newly added nodes in a growing network under the preferential attachment scheme based on popularity of the existing nodes. SIR dynamics is studied in networks with a fraction 1-p of the links removed. Extensive numerical simulations reveal that there exists a threshold pc such that for p≥pc, epidemic breaks out in the network. For p<pc, only a local spread results. The dependence of pc on β is studied in detail. The function pc(β) separates the space formed by β and p into regions corresponding to local and global spreads, respectively.

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.

scholarly journals Fixed Point Analysis of Kermack Mckendrick SIR Model

10.29007/pl65 ◽  
2018 ◽  
Author(s):  
Fenny Narsingani ◽  
Mahendra B Prajapati ◽  
Pravin Himmatlal Bhathawala
Keyword(s):  
Infectious Disease ◽  
Fixed Point ◽  
Threshold Value ◽  
Sir Model ◽  
Disease Spread ◽  
Term Outcome ◽  
Long Term Outcome ◽  
Point Analysis ◽  
Transmission Of Disease

Public health is constantly under risk due to growing microorganisms. Infectious disease spread rapidly among the population in contact and so people take the different steps to reduce the transmission of disease. Compartmental model such as SIR model developed by W. Kermack and G Mckendrick are modeled for the progress of epidemic. Fixed point analysis has been applied to mathematical models of compartmental infectious disease models for understanding the long term outcome of disease. We have applied the analysis to the spread of infectious disease and obtained the threshold value and this threshold value helps us to predict when epidemic peaks.

scholarly journals Fractal scale-free networks resistant to disease spread

2008 ◽  
Vol 2008 (09) ◽  
pp. P09008 ◽  
Author(s):  
Zhongzhi Zhang ◽  
Shuigeng Zhou ◽  
Tao Zou ◽  
Guisheng Chen
Keyword(s):  
Disease Spread ◽  
Scale Free ◽  
Scale Free Networks

scholarly journals An Economist’s Guide to Epidemiology Models of Infectious Disease

2020 ◽  
Vol 34 (4) ◽  
pp. 79-104
Author(s):  
Christopher Avery ◽  
William Bossert ◽  
Adam Clark ◽  
Glenn Ellison ◽  
Sara Fisher Ellison
Keyword(s):  
Infectious Disease ◽  
Political Economy ◽  
Disease Transmission ◽  
Sir Model ◽  
Disease Suppression ◽  
Disease Spread ◽  
High Profile ◽  
Models Of Disease ◽  
Susceptible Populations

We describe the structure and use of epidemiology models of disease transmission, with an emphasis on the susceptible/infected/recovered (SIR) model. We discuss high-profile forecasts of cases and deaths that have been based on these models, what went wrong with the early forecasts, and how they have adapted to the current COVID pandemic. We also offer three distinct areas where economists would be well positioned to contribute to or inform this epidemiology literature: modeling heterogeneity of susceptible populations in various dimensions, accommodating endogeneity of the parameters governing disease spread, and helping to understand the importance of political economy issues in disease suppression.

scholarly journals Protection Strategy against an Epidemic Disease on Edge-Weighted Graphs Applied to a COVID-19 Case

Biology ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 667
Author(s):  
Ronald Manríquez ◽  
Camilo Guerrero-Nancuante ◽  
Carla Taramasco
Keyword(s):  
Infectious Diseases ◽  
Sir Model ◽  
Weighted Graphs ◽  
Epidemic Disease ◽  
Ranking List ◽  
Weighted Network ◽  
Protection Strategy ◽  
Importance Ranking

Among the diverse and important applications that networks currently have is the modeling of infectious diseases. Immunization, or the process of protecting nodes in the network, plays a key role in stopping diseases from spreading. Hence the importance of having tools or strategies that allow the solving of this challenge. In this paper, we evaluate the effectiveness of the DIL-Wα ranking in immunizing nodes in an edge-weighted network with 3866 nodes and 6,841,470 edges. The network is obtained from a real database and the spread of COVID-19 was modeled with the classic SIR model. We apply the protection to the network, according to the importance ranking list produced by DIL-Wα, considering different protection budgets. Furthermore, we consider three different values for α; in this way, we compare how the protection performs according to the value of α.

A Study of Computer Virus Propagation on Scale Free Networks Using Differential Equations

2016 ◽  
pp. 196-214
Author(s):  
Mohammad S. Khan
Keyword(s):  
Differential Equations ◽  
Infection Rate ◽  
Death Rate ◽  
Sir Model ◽  
Computer Virus ◽  
Virus Propagation ◽  
Excess Death ◽  
Scale Free ◽  
Scale Free Networks ◽  
Simulation Results

The SIR model is used extensively in the field of epidemiology, in particular, for the analysis of communal diseases. One problem with SIR and other existing models is that they are tailored to random or Erdos type networks since they do not consider the varying probabilities of infection or immunity per node. In this paper, we present the application and the simulation results of the pSEIRS model that takes into account the probabilities, and is thus suitable for more realistic scale free networks. In the pSEIRS model, the death rate and the excess death rate are constant for infective nodes. Latent and immune periods are assumed to be constant and the infection rate is assumed to be a function of the size of the total population and the size of the infected population. A node recovers from an infection temporarily with a probability p and dies from the infection with probability (1-p).

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