Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks

Kostova, Tanya

doi:10.1080/10236190902766835

Title: Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks

Abstract

We present and analyze a discrete-time susceptible-infected epidemic network model which represents each host as a separate entity and allows heterogeneous hosts and contacts. We establish a necessary and sufficient condition for global stability of the disease-free equilibrium of the system (defined as epidemic controllability) which defines the epidemic reproduction number of the network. When this condition is not fulfilled, we show that the system has a unique, locally stable equilibrium. As a result, we further derive sufficient conditions for epidemic controllability in terms of the epidemic rates and the network topology.

Authors:

Kostova, Tanya ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: Fri Jul 09 00:00:00 EDT 2010

Research Org.:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1343012

Report Number(s):: LLNL-JRNL-404031
Journal ID: ISSN 1023-6198

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Difference Equations and Applications

Additional Journal Information:: Journal Volume: 15; Journal Issue: 4; Journal ID: ISSN 1023-6198

Publisher:: Taylor & Francis

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 99 GENERAL AND MISCELLANEOUS; epidemic network; network dynamics; connectivity; epidemic control; dynamical system; reproduction number

Citation Formats


                    Kostova, Tanya. Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks.  United States: N. p., 2010. 
Web.  doi:10.1080/10236190902766835.

Copy to clipboard


                    Kostova, Tanya. Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks.  United States.  https://doi.org/10.1080/10236190902766835

Copy to clipboard


                    Kostova, Tanya. Fri .  
"Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks".  United States.  https://doi.org/10.1080/10236190902766835.  https://www.osti.gov/servlets/purl/1343012.

Copy to clipboard


                    
@article{osti_1343012,

  title        = {Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks},

  author       = {Kostova, Tanya},

  abstractNote = {We present and analyze a discrete-time susceptible-infected epidemic network model which represents each host as a separate entity and allows heterogeneous hosts and contacts. We establish a necessary and sufficient condition for global stability of the disease-free equilibrium of the system (defined as epidemic controllability) which defines the epidemic reproduction number of the network. When this condition is not fulfilled, we show that the system has a unique, locally stable equilibrium. As a result, we further derive sufficient conditions for epidemic controllability in terms of the epidemic rates and the network topology.},

  doi          = {10.1080/10236190902766835},

  journal      = {Journal of Difference Equations and Applications},

  number       = 4,

  volume       = 15,

  place        = {United States},

  year         = {Fri Jul 09 00:00:00 EDT 2010},

  month        = {Fri Jul 09 00:00:00 EDT 2010}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1080/10236190902766835

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 8 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Epidemic dynamics and endemic states in complex networks
journal, May 2001

Pastor-Satorras, Romualdo; Vespignani, Alessandro
Physical Review E, Vol. 63, Issue 6
DOI: 10.1103/PhysRevE.63.066117

Susceptible–infected–recovered epidemics in dynamic contact networks
journal, September 2007

Volz, Erik; Meyers, Lauren Ancel
Proceedings of the Royal Society B: Biological Sciences, Vol. 274, Issue 1628
DOI: 10.1098/rspb.2007.1159

Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
journal, November 2002

van den Driessche, P.; Watmough, James
Mathematical Biosciences, Vol. 180, Issue 1-2
DOI: 10.1016/S0025-5564(02)00108-6

Bounds for the Perron root of a nonnegative matrix involving the properties of its graph
journal, October 1995

Al'pin, Yu. A.
Mathematical Notes, Vol. 58, Issue 4
DOI: 10.1007/BF02305101

Stability of the endemic equilibrium in epidemic models with subpopulations
journal, August 1985

Hethcote, Herbert W.; Thieme, Horst R.
Mathematical Biosciences, Vol. 75, Issue 2
DOI: 10.1016/0025-5564(85)90038-0

The role of the airline transportation network in the prediction and predictability of global epidemics
journal, February 2006

Colizza, Vittoria; Barrat, Alain; Barthélemy, Marc
Proceedings of the National Academy of Sciences, Vol. 103, Issue 7
DOI: 10.1073/pnas.0510525103

Epidemic spreading in correlated complex networks
journal, October 2002

Boguñá, Marián; Pastor-Satorras, Romualdo
Physical Review E, Vol. 66, Issue 4
DOI: 10.1103/PhysRevE.66.047104

Epidemic Spreading in Scale-Free Networks
journal, April 2001

Pastor-Satorras, Romualdo; Vespignani, Alessandro
Physical Review Letters, Vol. 86, Issue 14
DOI: 10.1103/PhysRevLett.86.3200

Applications of Perron-Frobenius theory to population dynamics
journal, May 2002

Li, Chi-Kwong; Schneider, Hans
Journal of Mathematical Biology, Vol. 44, Issue 5
DOI: 10.1007/s002850100132

Epidemic thresholds in real networks
journal, January 2008

Chakrabarti, Deepayan; Wang, Yang; Wang, Chenxi
ACM Transactions on Information and System Security, Vol. 10, Issue 4
DOI: 10.1145/1284680.1284681

Networks and epidemic models
journal, May 2005

Keeling, Matt J.; Eames, Ken T. D.
Journal of The Royal Society Interface, Vol. 2, Issue 4
DOI: 10.1098/rsif.2005.0051

Containing a large bioterrorist smallpox attack: a computer simulation approach
journal, March 2007

Longini, Ira M.; Elizabeth Halloran, M.; Nizam, Azhar
International Journal of Infectious Diseases, Vol. 11, Issue 2
DOI: 10.1016/j.ijid.2006.03.002

Predicting epidemics on directed contact networks
journal, June 2006

Meyers, Lauren Ancel; Newman, M. E. J.; Pourbohloul, Babak
Journal of Theoretical Biology, Vol. 240, Issue 3
DOI: 10.1016/j.jtbi.2005.10.004

Works referencing / citing this record:

When is connectivity important? A case study of the spatial pattern of sudden oak death
journal, March 2010

Ellis, Alicia M.; Václavík, Tomáš; Meentemeyer, Ross K.
Oikos, Vol. 119, Issue 3
DOI: 10.1111/j.1600-0706.2009.17918.x

Epidemic Threshold of an SIS Model in Dynamic Switching Networks
journal, March 2016

Sanatkar, Mohammad Reza; White, Warren N.; Natarajan, Balasubramaniam
IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 46, Issue 3
DOI: 10.1109/tsmc.2015.2448061

Connecting Network Properties of Rapidly Disseminating Epizoonotics
journal, June 2012

Rivas, Ariel L.; Fasina, Folorunso O.; Hoogesteyn, Almira L.
PLoS ONE, Vol. 7, Issue 6
DOI: 10.1371/journal.pone.0039778

Similar Records in DOE PAGES and OSTI.GOV collections:

A Suite of Mechanistic Epidemiological Decision Support Tools

Journal Article Fenimore, Paul ; McMahon, Benjamin ; Hengartner, Nicolas ; ... - Online Journal of Public Health Informatics

Objective: We will demonstrate tools that allow mechanistic contraints on disease progression and epidemic spread to play off against interventions, mitigation, and control measures. The fundamental mechanisms of disease progression and epidemic spread provide important constraints on interpreting changing epidemic cases counts with time and geography in the context of on-going interventions, mitigations, and controls. Models such as these that account for the effects of human actions can also allow evaluation of the importance of categories of epidemic and disease controls. Introduction: We present the EpiEarly, EpiGrid, and EpiCast tools for mechanistically-based biological decision support. The range of tools coversmore »« less
https://doi.org/10.5210/ojphi.v10i1.8299

Full Text Available
Time-dependent heterogeneity leads to transient suppression of the COVID-19 epidemic, not herd immunity

Journal Article Tkachenko, Alexei V. ; Maslov, Sergei ; Elbanna, Ahmed ; ... - Proceedings of the National Academy of Sciences of the United States of America

Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, superspreading events lead to burstiness and overdispersion, whereas long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in both the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both timescales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through reparameterization. We derive a nonlinear dependence of the effective reproduction number R_e on the susceptible population fraction S. We showmore »« less
https://doi.org/10.1073/pnas.2015972118
Connecting Network Properties of Rapidly Disseminating Epizoonotics

Journal Article Rivas, Ariel L. ; Fasina, Folorunso O. ; Hoogesteyn, Almira L. ; ... - PLoS ONE

Background: To effectively control the geographical dissemination of infectious diseases, their properties need to be determined. To test that rapid microbial dispersal requires not only susceptible hosts but also a pre-existing, connecting network, we explored constructs meant to reveal the network properties associated with disease spread, which included the road structure. Methods: Using geo-temporal data collected from epizoonotics in which all hosts were susceptible (mammals infected by Foot-and-mouth disease virus, Uruguay, 2001; birds infected by Avian Influenza virus H5N1, Nigeria, 2006), two models were compared: 1) ‘connectivity’, a model that integrated bio-physical concepts (the agent’s transmission cycle, road topology) intomore »« less
https://doi.org/10.1371/journal.pone.0039778

Full Text Available
Epidemic spreading in time-varying community networks

Journal Article Ren, Guangming ; Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024 ; Wang, Xingyuan - Chaos (Woodbury, N. Y.)

The spreading processes of many infectious diseases have comparable time scale as the network evolution. Here, we present a simple networks model with time-varying community structure, and investigate susceptible-infected-susceptible epidemic spreading processes in this model. By both theoretic analysis and numerical simulations, we show that the efficiency of epidemic spreading in this model depends intensively on the mobility rate q of the individuals among communities. We also find that there exists a mobility rate threshold q{sub c}. The epidemic will survive when q > q{sub c} and die when q < q{sub c}. These results can help understanding the impacts of human travel onmore »« less
https://doi.org/10.1063/1.4876436
Inference of Transmission Network Structure from HIV Phylogenetic Trees

Journal Article Giardina, Federica ; Romero-Severson, Ethan Obie ; Albert, Jan ; ... - PLoS Computational Biology (Online)

Phylogenetic inference is an attractive means to reconstruct transmission histories and epidemics. However, there is not a perfect correspondence between transmission history and virus phylogeny. Both node height and topological differences may occur, depending on the interaction between within-host evolutionary dynamics and between-host transmission patterns. To investigate these interactions, we added a within-host evolutionary model in epidemiological simulations and examined if the resulting phylogeny could recover different types of contact networks. To further improve realism, we also introduced patient-specific differences in infectivity across disease stages, and on the epidemic level we considered incomplete sampling and the age of the epidemic.more »« less
Cited by 18
https://doi.org/10.1371/journal.pcbi.1005316

Full Text Available

Similar Records

Title: Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks

Abstract

Citation Formats

Epidemic dynamics and endemic states in complex networks journal, May 2001

Susceptible–infected–recovered epidemics in dynamic contact networks journal, September 2007

Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission journal, November 2002

Bounds for the Perron root of a nonnegative matrix involving the properties of its graph journal, October 1995

Stability of the endemic equilibrium in epidemic models with subpopulations journal, August 1985

The role of the airline transportation network in the prediction and predictability of global epidemics journal, February 2006

Epidemic spreading in correlated complex networks journal, October 2002

Epidemic Spreading in Scale-Free Networks journal, April 2001

Applications of Perron-Frobenius theory to population dynamics journal, May 2002

Epidemic thresholds in real networks journal, January 2008

Networks and epidemic models journal, May 2005

Containing a large bioterrorist smallpox attack: a computer simulation approach journal, March 2007

Predicting epidemics on directed contact networks journal, June 2006

When is connectivity important? A case study of the spatial pattern of sudden oak death journal, March 2010

Epidemic Threshold of an SIS Model in Dynamic Switching Networks journal, March 2016

Connecting Network Properties of Rapidly Disseminating Epizoonotics journal, June 2012

Epidemic dynamics and endemic states in complex networks
journal, May 2001

Susceptible–infected–recovered epidemics in dynamic contact networks
journal, September 2007

Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
journal, November 2002

Bounds for the Perron root of a nonnegative matrix involving the properties of its graph
journal, October 1995

Stability of the endemic equilibrium in epidemic models with subpopulations
journal, August 1985

The role of the airline transportation network in the prediction and predictability of global epidemics
journal, February 2006

Epidemic spreading in correlated complex networks
journal, October 2002

Epidemic Spreading in Scale-Free Networks
journal, April 2001

Applications of Perron-Frobenius theory to population dynamics
journal, May 2002

Epidemic thresholds in real networks
journal, January 2008

Networks and epidemic models
journal, May 2005

Containing a large bioterrorist smallpox attack: a computer simulation approach
journal, March 2007

Predicting epidemics on directed contact networks
journal, June 2006

When is connectivity important? A case study of the spatial pattern of sudden oak death
journal, March 2010

Epidemic Threshold of an SIS Model in Dynamic Switching Networks
journal, March 2016

Connecting Network Properties of Rapidly Disseminating Epizoonotics
journal, June 2012