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An Exact Relationship Between Invasion Probability and Endemic Prevalence for Markovian SIS Dynamics on Networks

Understanding models which represent the invasion of network-based systems by infectious agents can give important insights into many real-world situations, including the prevention and control of infectious diseases and computer viruses. Here we consider Markovian susceptible-infectious-susceptible...

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Autores principales: Wilkinson, Robert R., Sharkey, Kieran J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2013
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3728314/
https://www.ncbi.nlm.nih.gov/pubmed/23935916
http://dx.doi.org/10.1371/journal.pone.0069028
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author Wilkinson, Robert R.
Sharkey, Kieran J.
author_facet Wilkinson, Robert R.
Sharkey, Kieran J.
author_sort Wilkinson, Robert R.
collection PubMed
description Understanding models which represent the invasion of network-based systems by infectious agents can give important insights into many real-world situations, including the prevention and control of infectious diseases and computer viruses. Here we consider Markovian susceptible-infectious-susceptible (SIS) dynamics on finite strongly connected networks, applicable to several sexually transmitted diseases and computer viruses. In this context, a theoretical definition of endemic prevalence is easily obtained via the quasi-stationary distribution (QSD). By representing the model as a percolation process and utilising the property of duality, we also provide a theoretical definition of invasion probability. We then show that, for undirected networks, the probability of invasion from any given individual is equal to the (probabilistic) endemic prevalence, following successful invasion, at the individual (we also provide a relationship for the directed case). The total (fractional) endemic prevalence in the population is thus equal to the average invasion probability (across all individuals). Consequently, for such systems, the regions or individuals already supporting a high level of infection are likely to be the source of a successful invasion by another infectious agent. This could be used to inform targeted interventions when there is a threat from an emerging infectious disease.
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spelling pubmed-37283142013-08-09 An Exact Relationship Between Invasion Probability and Endemic Prevalence for Markovian SIS Dynamics on Networks Wilkinson, Robert R. Sharkey, Kieran J. PLoS One Research Article Understanding models which represent the invasion of network-based systems by infectious agents can give important insights into many real-world situations, including the prevention and control of infectious diseases and computer viruses. Here we consider Markovian susceptible-infectious-susceptible (SIS) dynamics on finite strongly connected networks, applicable to several sexually transmitted diseases and computer viruses. In this context, a theoretical definition of endemic prevalence is easily obtained via the quasi-stationary distribution (QSD). By representing the model as a percolation process and utilising the property of duality, we also provide a theoretical definition of invasion probability. We then show that, for undirected networks, the probability of invasion from any given individual is equal to the (probabilistic) endemic prevalence, following successful invasion, at the individual (we also provide a relationship for the directed case). The total (fractional) endemic prevalence in the population is thus equal to the average invasion probability (across all individuals). Consequently, for such systems, the regions or individuals already supporting a high level of infection are likely to be the source of a successful invasion by another infectious agent. This could be used to inform targeted interventions when there is a threat from an emerging infectious disease. Public Library of Science 2013-07-30 /pmc/articles/PMC3728314/ /pubmed/23935916 http://dx.doi.org/10.1371/journal.pone.0069028 Text en © 2013 Wilkinson, Sharkey http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
spellingShingle Research Article
Wilkinson, Robert R.
Sharkey, Kieran J.
An Exact Relationship Between Invasion Probability and Endemic Prevalence for Markovian SIS Dynamics on Networks
title An Exact Relationship Between Invasion Probability and Endemic Prevalence for Markovian SIS Dynamics on Networks
title_full An Exact Relationship Between Invasion Probability and Endemic Prevalence for Markovian SIS Dynamics on Networks
title_fullStr An Exact Relationship Between Invasion Probability and Endemic Prevalence for Markovian SIS Dynamics on Networks
title_full_unstemmed An Exact Relationship Between Invasion Probability and Endemic Prevalence for Markovian SIS Dynamics on Networks
title_short An Exact Relationship Between Invasion Probability and Endemic Prevalence for Markovian SIS Dynamics on Networks
title_sort exact relationship between invasion probability and endemic prevalence for markovian sis dynamics on networks
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3728314/
https://www.ncbi.nlm.nih.gov/pubmed/23935916
http://dx.doi.org/10.1371/journal.pone.0069028
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