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

Wilkinson, RR and Sharkey, KJ (2013) An Exact Relationship Between Invasion Probability and Endemic Prevalence for Markovian SIS Dynamics on Networks. PLoS One, 8 (7). ISSN 1932-6203

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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.

Item Type: Article
Uncontrolled Keywords: MD Multidisciplinary
Subjects: Q Science > QA Mathematics
Divisions: Applied Mathematics (merged with Comp Sci 10 Aug 20)
Publisher: Public Library of Science
Date Deposited: 03 Jul 2019 10:05
Last Modified: 03 Sep 2021 22:53
DOI or ID number: 10.1371/journal.pone.0069028
URI: https://researchonline.ljmu.ac.uk/id/eprint/10966
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