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<!DOCTYPE html> <html > <head> <meta charset="utf-8"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <meta content="width=device-width, initial-scale=1" name="viewport"> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs"> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="vC7C-6YyQgD7K4OUrlRUHTSW6bSLo0xBIRUlh939782z_ioKNjOGO5GeEHaQOUBjgjU6nkHwJXuIANyAE-18Iw" /> <meta name="citation_title" content="Influence of vaccination strategies and topology on the herd immunity of complex networks" /> <meta name="citation_author" content="Mahendra Piraveenan" /> <meta name="twitter:card" content="summary" /> <meta name="twitter:url" content="https://www.academia.edu/32495855/Influence_of_vaccination_strategies_and_topology_on_the_herd_immunity_of_complex_networks" /> <meta name="twitter:title" content="Influence of vaccination strategies and topology on the herd immunity of complex networks" /> <meta name="twitter:description" content="It is well known that non-vaccinated individuals may be protected from contacting a disease by vaccinated individuals in a social network through community protection (herd immunity). Such protection greatly depends on the underlying topology of the" /> <meta name="twitter:image" content="https://0.academia-photos.com/84035/23405/18543896/s200_mahendra.piraveenan.jpg" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/32495855/Influence_of_vaccination_strategies_and_topology_on_the_herd_immunity_of_complex_networks" /> <meta property="og:title" content="Influence of vaccination strategies and topology on the herd immunity of complex networks" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="It is well known that non-vaccinated individuals may be protected from contacting a disease by vaccinated individuals in a social network through community protection (herd immunity). Such protection greatly depends on the underlying topology of the" /> <meta property="article:author" content="https://sydney.academia.edu/MahendraPiraveenan" /> <meta name="description" content="It is well known that non-vaccinated individuals may be protected from contacting a disease by vaccinated individuals in a social network through community protection (herd immunity). Such protection greatly depends on the underlying topology of the" /> <title>(PDF) Influence of vaccination strategies and topology on the herd immunity of complex networks</title> <link rel="canonical" href="https://www.academia.edu/32495855/Influence_of_vaccination_strategies_and_topology_on_the_herd_immunity_of_complex_networks" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = 'b092bf3a3df71cf13feee7c143e83a57eb6b94fb'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1739827400000); window.Aedu.timeDifference = new Date().getTime() - 1739827400000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"It is well known that non-vaccinated individuals may be protected from contacting a disease by vaccinated individuals in a social network through community protection (herd immunity). Such protection greatly depends on the underlying topology of the social network, the strategy used in selecting individuals for vaccination, and the interplay between these. In this paper, we analyse how the interplay between topology and immunization strategies influences the herd immunity of social networks. First, we introduce an area under curve measure which can quantify the levels of herd immunity in a social network. Then, using this measure, we analyse the above mentioned interplay in three ways: (1) by comparing vaccination strategies across topologies, (2) by analysing the influence of selected topological metrics, and (3) by considering the influence of network growth on herd immunity. For qualitative comparison, we consider three classical topologies (scale-free, random, and small-world) and three vaccination strategies (natural, random, and betweenness-based immunization). We show that betweenness-based vaccination is the best strategy of immunization in static networks , regardless of topology, but its prominence over other strategies diminishes in dynamically growing topologies. We find that the network features that lead to \u0026amp;#39;small-worldness\u0026amp;#39; in networks (low diameter and high clustering) discourage herd immunity, regardless of the vaccination strategy, while preferential mixing (high as-sortativity) encourages it. In terms of growth, we demonstrate that herd immunity of random networks actually increases with growth, if the proportion of survivors to a secondary infection is considered, while the community protection in scale-free and small-world networks decreases with growth. Our work highlights the complex balance between social network structure and vaccination strategies in influencing community protection, and contributes a numerical measure to quantify this. Keywords Complex systems Á Structures and organization in complex systems Á Systems obeying scaling laws Á Graph theory Á Networks and genealogical trees","author":[{"@context":"https://schema.org","@type":"Person","name":"Mahendra Piraveenan","url":"https://sydney.academia.edu/MahendraPiraveenan"}],"contributor":[],"dateCreated":"2017-04-18","dateModified":"2017-04-19","headline":"Influence of vaccination strategies and topology on the herd immunity of complex networks","image":"https://attachments.academia-assets.com/52681954/thumbnails/1.jpg","inLanguage":"en","keywords":["Social Networks","Social Networking","Social Network Analysis (SNA)","Vaccination","Herd Immunity","centrality and vaccination","betweenenss and vaccination","betweenness and vaccination","vaccination in social networks"],"publisher":{"@context":"https://schema.org","@type":"Organization","name":null},"sourceOrganization":[{"@context":"https://schema.org","@type":"EducationalOrganization","name":"sydney"}],"thumbnailUrl":"https://attachments.academia-assets.com/52681954/thumbnails/1.jpg","url":"https://www.academia.edu/32495855/Influence_of_vaccination_strategies_and_topology_on_the_herd_immunity_of_complex_networks"}</script><style type="text/css">@media(max-width: 567px){:root{--token-mode: Rebrand;--dropshadow: 0 2px 4px 0 #22223340;--primary-brand: #0645b1;--error-dark: #b60000;--success-dark: #05b01c;--inactive-fill: #ebebee;--hover: #0c3b8d;--pressed: #082f75;--button-primary-fill-inactive: #ebebee;--button-primary-fill: #0645b1;--button-primary-text: #ffffff;--button-primary-fill-hover: #0c3b8d;--button-primary-fill-press: #082f75;--button-primary-icon: #ffffff;--button-primary-fill-inverse: #ffffff;--button-primary-text-inverse: #082f75;--button-primary-icon-inverse: 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window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":32495855,"created_at":"2017-04-18T22:02:17.872-07:00","from_world_paper_id":null,"updated_at":"2021-01-14T16:30:05.332-08:00","_data":{"abstract":"It is well known that non-vaccinated individuals may be protected from contacting a disease by vaccinated individuals in a social network through community protection (herd immunity). Such protection greatly depends on the underlying topology of the social network, the strategy used in selecting individuals for vaccination, and the interplay between these. In this paper, we analyse how the interplay between topology and immunization strategies influences the herd immunity of social networks. First, we introduce an area under curve measure which can quantify the levels of herd immunity in a social network. Then, using this measure, we analyse the above mentioned interplay in three ways: (1) by comparing vaccination strategies across topologies, (2) by analysing the influence of selected topological metrics, and (3) by considering the influence of network growth on herd immunity. For qualitative comparison, we consider three classical topologies (scale-free, random, and small-world) and three vaccination strategies (natural, random, and betweenness-based immunization). We show that betweenness-based vaccination is the best strategy of immunization in static networks , regardless of topology, but its prominence over other strategies diminishes in dynamically growing topologies. We find that the network features that lead to 'small-worldness' in networks (low diameter and high clustering) discourage herd immunity, regardless of the vaccination strategy, while preferential mixing (high as-sortativity) encourages it. In terms of growth, we demonstrate that herd immunity of random networks actually increases with growth, if the proportion of survivors to a secondary infection is considered, while the community protection in scale-free and small-world networks decreases with growth. Our work highlights the complex balance between social network structure and vaccination strategies in influencing community protection, and contributes a numerical measure to quantify this. Keywords Complex systems Á Structures and organization in complex systems Á Systems obeying scaling laws Á Graph theory Á Networks and genealogical trees"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Influence of vaccination strategies and topology on the herd immunity of complex networks","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [84035]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":52681954,"attachmentType":"pdf"}"><img alt="First page of “Influence of vaccination strategies and topology on the herd immunity of complex networks”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/52681954/mini_magick20190122-11852-1vg78kk.png?1548198802" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Influence of vaccination strategies and topology on the herd immunity of complex networks</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="84035" href="https://sydney.academia.edu/MahendraPiraveenan"><img alt="Profile image of Mahendra Piraveenan" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/84035/23405/18543896/s65_mahendra.piraveenan.jpg" />Mahendra Piraveenan</a></div><div class="ds-work-card--detail"><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">16 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 32495855; 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if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">It is well known that non-vaccinated individuals may be protected from contacting a disease by vaccinated individuals in a social network through community protection (herd immunity). Such protection greatly depends on the underlying topology of the social network, the strategy used in selecting individuals for vaccination, and the interplay between these. In this paper, we analyse how the interplay between topology and immunization strategies influences the herd immunity of social networks. First, we introduce an area under curve measure which can quantify the levels of herd immunity in a social network. Then, using this measure, we analyse the above mentioned interplay in three ways: (1) by comparing vaccination strategies across topologies, (2) by analysing the influence of selected topological metrics, and (3) by considering the influence of network growth on herd immunity. For qualitative comparison, we consider three classical topologies (scale-free, random, and small-world) and three vaccination strategies (natural, random, and betweenness-based immunization). We show that betweenness-based vaccination is the best strategy of immunization in static networks , regardless of topology, but its prominence over other strategies diminishes in dynamically growing topologies. We find that the network features that lead to 'small-worldness' in networks (low diameter and high clustering) discourage herd immunity, regardless of the vaccination strategy, while preferential mixing (high as-sortativity) encourages it. In terms of growth, we demonstrate that herd immunity of random networks actually increases with growth, if the proportion of survivors to a secondary infection is considered, while the community protection in scale-free and small-world networks decreases with growth. Our work highlights the complex balance between social network structure and vaccination strategies in influencing community protection, and contributes a numerical measure to quantify this. Keywords Complex systems Á Structures and organization in complex systems Á Systems obeying scaling laws Á Graph theory Á Networks and genealogical trees</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":52681954,"attachmentType":"pdf","workUrl":"https://www.academia.edu/32495855/Influence_of_vaccination_strategies_and_topology_on_the_herd_immunity_of_complex_networks"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":52681954,"attachmentType":"pdf","workUrl":"https://www.academia.edu/32495855/Influence_of_vaccination_strategies_and_topology_on_the_herd_immunity_of_complex_networks"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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Such protection greatly depends on the underlying topology of the social network, and the strategy used in selecting individuals for vaccination. Social networks however undergo constant growth, and it may be argued that network growth may change the level of herd immunity present in social networks. In this paper, we analyse the effect of growth and immunization strategies on herd immunity of social networks. Considering three classical topologies -Random, scale-free and small-world, we compare the influence of immunization strategies on each of them and then discuss how network growth can nullify or amplify these differences. We show that betweenness based vaccination is best strategy of immunization, regardless of topology, in static networks, but its prominence over other strategies diminishes in dynamically growing topologies. We demonstrate that herd immunity of random networks actually increases with growth, if the proportion of survivors to a secondary infection is considered, while the community protection in scale-free and small world networks decreases with growth. We compare the relative influence of growth on each class of networks vaccinated under different strategies.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Effect of vaccination strategies on the herd immunity of growing networks","attachmentId":32001255,"attachmentType":"pdf","work_url":"https://www.academia.edu/4657360/Effect_of_vaccination_strategies_on_the_herd_immunity_of_growing_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/4657360/Effect_of_vaccination_strategies_on_the_herd_immunity_of_growing_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="120877803" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/120877803/Global_efficiency_of_local_immunization_on_complex_networks">Global efficiency of local immunization on complex networks</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="143525165" href="https://ulaval.academia.edu/LouisJDub%C3%A9">Louis J. Dubé</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Scientific reports, 2013</p><p class="ds-related-work--abstract ds2-5-body-sm">Epidemics occur in all shapes and forms: infections propagating in our sparse sexual networks, rumours and diseases spreading through our much denser social interactions, or viruses circulating on the Internet. With the advent of large databases and efficient analysis algorithms, these processes can be better predicted and controlled. In this study, we use different characteristics of network organization to identify the influential spreaders in 17 empirical networks of diverse nature using 2 epidemic models. We find that a judicious choice of local measures, based either on the network&#39;s connectivity at a microscopic scale or on its community structure at a mesoscopic scale, compares favorably to global measures, such as betweenness centrality, in terms of efficiency, practicality and robustness. We also develop an analytical framework that highlights a transition in the characteristic scale of different epidemic regimes. This allows to decide which local measure should govern ...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Global efficiency of local immunization on complex networks","attachmentId":115891482,"attachmentType":"pdf","work_url":"https://www.academia.edu/120877803/Global_efficiency_of_local_immunization_on_complex_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/120877803/Global_efficiency_of_local_immunization_on_complex_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="112318359" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/112318359/Immunization_Strategies_Based_on_the_Overlapping_Nodes_in_Networks_with_Community_Structure">Immunization Strategies Based on the Overlapping Nodes in Networks with Community Structure</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="621317" href="https://u-bourgogne.academia.edu/hocinecherifi">Hocine Cherifi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Computational Social Networks, 2016</p><p class="ds-related-work--abstract ds2-5-body-sm">Understanding how the network topology affects the spread of an epidemic is a main concern in order to develop efficient immunization strategies. While there is a great deal of work dealing with the macroscopic topological properties of the networks, few studies have been devoted to the influence of the community structure. Furthermore, while in many real-world networks communities may overlap, in these studies non-overlapping community structures are considered. In order to gain insight about the influence of the overlapping nodes in the epidemic process we conduct an empirical evaluation of basic deterministic immunization strategies based on the overlapping nodes.Using the classical SIR model on a real-world network with ground truth overlapping community structure we analyse how immunization based on the membership number of overlapping nodes (which is the number of communities the node belongs to) affect the largest connected component size. Comparison with random immunization strategies designed for networks with non-overlapping community structure show that overlapping nodes play a major role in the epidemic process.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Immunization Strategies Based on the Overlapping Nodes in Networks with Community Structure","attachmentId":109585194,"attachmentType":"pdf","work_url":"https://www.academia.edu/112318359/Immunization_Strategies_Based_on_the_Overlapping_Nodes_in_Networks_with_Community_Structure","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/112318359/Immunization_Strategies_Based_on_the_Overlapping_Nodes_in_Networks_with_Community_Structure"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="17939435" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/17939435/Network_frailty_and_the_geometry_of_herd_immunity">Network frailty and the geometry of herd immunity</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="37853997" href="https://independent.academia.edu/LaurenMeyers1">Lauren Meyers</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proceedings of the Royal Society B: Biological Sciences, 2006</p><p class="ds-related-work--abstract ds2-5-body-sm">The spread of infectious disease through communities depends fundamentally on the underlying patterns of contacts between individuals. Generally, the more contacts one individual has, the more vulnerable they are to infection during an epidemic. Thus, outbreaks disproportionately impact the most highly connected demographics. Epidemics can then lead, through immunization or removal of individuals, to sparser networks that are more resistant to future transmission of a given disease. Using several classes of contact networks-Poisson, scale-free and small-world-we characterize the structural evolution of a network due to an epidemic in terms of frailty (the degree to which highly connected individuals are more vulnerable to infection) and interference (the extent to which the epidemic cuts off connectivity among the susceptible population that remains following an epidemic). The evolution of the susceptible network over the course of an epidemic differs among the classes of networks; frailty, relative to interference, accounts for an increasing component of network evolution on networks with greater variance in contacts. The result is that immunization due to prior epidemics can provide greater community protection than random vaccination on networks with heterogeneous contact patterns, while the reverse is true for highly structured populations.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Network frailty and the geometry of herd immunity","attachmentId":39789429,"attachmentType":"pdf","work_url":"https://www.academia.edu/17939435/Network_frailty_and_the_geometry_of_herd_immunity","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/17939435/Network_frailty_and_the_geometry_of_herd_immunity"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="50524698" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/50524698/Immunization_of_networks_with_non_overlapping_community_structure">Immunization of networks with non-overlapping community structure</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="621317" href="https://u-bourgogne.academia.edu/hocinecherifi">Hocine Cherifi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Social Network Analysis and Mining</p><p class="ds-related-work--abstract ds2-5-body-sm">Although community structure is ubiquitous in complex networks, few works exploit this topological property to control epidemics. In this work, devoted to networks with non-overlapping community structure (i.e, a node belongs to a single community), we propose and investigate three global immunization strategies. In order to characterize the influence of a node, various pieces of information are used such as the number of communities that the node can reach in one hop, the nature of the links (intra community links, inter community links), the size of the communities, and the interconnection density between communities. Numerical simulations with the Susceptible-Infected-Removed (SIR) epidemiological model are conducted on both real-world and synthetic networks. Experimental results show that the proposed strategies are more effective than classical alternatives that are agnostic of the community structure. Additionally, they outperform alternative local and global strategies designed for modular networks.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Immunization of networks with non-overlapping community structure","attachmentId":68475052,"attachmentType":"pdf","work_url":"https://www.academia.edu/50524698/Immunization_of_networks_with_non_overlapping_community_structure","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/50524698/Immunization_of_networks_with_non_overlapping_community_structure"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="125841255" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/125841255/Evolutionary_vaccination_dilemma_in_complex_networks">Evolutionary vaccination dilemma in complex networks</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="317834167" href="https://independent.academia.edu/AlessioCardillo1">Alessio Cardillo</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2013</p><p class="ds-related-work--abstract ds2-5-body-sm">In this work we analyze the evolution of voluntary vaccination in networked populations by entangling the spreading dynamics of an influenza-like disease with an evolutionary framework taking place at the end of each influenza season so that individuals take or not the vaccine upon their previous experience. Our framework thus put in competition two well-known dynamical properties of scale-free networks: the fast propagation of diseases and the promotion of cooperative behaviors. Our results show that when vaccine is perfect scale-free networks enhance the vaccination behavior with respect to random graphs with homogeneous connectivity patterns. However, when imperfection appears we find a cross-over effect so that the number of infected (vaccinated) individuals increases (decreases) with respect to homogeneous networks, thus showing up the competition between the aforementioned properties of scale-free graphs.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Evolutionary vaccination dilemma in complex networks","attachmentId":119811790,"attachmentType":"pdf","work_url":"https://www.academia.edu/125841255/Evolutionary_vaccination_dilemma_in_complex_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/125841255/Evolutionary_vaccination_dilemma_in_complex_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="91338358" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/91338358/Reactive_immunization_on_complex_networks">Reactive immunization on complex networks</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="12976326" href="https://unisalento.academia.edu/eleonoraalfinito">eleonora alfinito</a></div><p class="ds-related-work--metadata ds2-5-body-xs">EPL (Europhysics Letters), 2017</p><p class="ds-related-work--abstract ds2-5-body-sm">Epidemic spreading on complex networks depends on the topological structure as well as on the dynamical properties of the infection itself. Generally speaking, highly connected individuals play the role of hubs and are crucial to channel information across the network. On the other hand, static topological quantities measuring the connectivity structure are independent on the dynamical mechanisms of the infection. A natural question is therefore how to improve the topological analysis by some kind of dynamical information that may be extracted from the ongoing infection itself. In this spirit, we propose a novel vaccination scheme that exploits information from the details of the infection pattern at the moment when the vaccination strategy is applied. Numerical simulations of the infection process show that the proposed immunization strategy is effective and robust on a wide class of complex networks.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Reactive immunization on complex networks","attachmentId":94654084,"attachmentType":"pdf","work_url":"https://www.academia.edu/91338358/Reactive_immunization_on_complex_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/91338358/Reactive_immunization_on_complex_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="79098213" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/79098213/Impact_of_network_assortativity_on_epidemic_and_vaccination">Impact of network assortativity on epidemic and vaccination</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="65576426" href="https://sydney.academia.edu/MikhailProkopenko">Mikhail Prokopenko</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Chaos, Solitons and Fractals, 2020</p><p class="ds-related-work--abstract ds2-5-body-sm">The resurgence of measles is largely attributed to the decline in vaccine adoption and the increase in mobility. Although the vaccine for measles is readily available and highly successful, its current adoption is not adequate to prevent epidemics. Vaccine adoption is directly affected by individual vaccination de- cisions, and has a complex interplay with the spatial spread of disease shaped by an underlying mobility (travelling) network. In this paper, we model the travelling connectivity as a scale-free network, and in- vestigate dependencies between the network’s assortativity and the resultant epidemic and vaccination dynamics. In doing so we extend an SIR-network model with game-theoretic components, capturing the imitation dynamics under a voluntary vaccination scheme. Our results show a correlation between the epidemic dynamics and the network’s assortativity, highlighting that networks with high assortativity tend to suppress epidemics under certain conditions. In highly assortative networks, the suppression is sustained producing an early convergence to equilibrium. In highly disassortative networks, however, the suppression effect diminishes over time due to scattering of non-vaccinating nodes, and frequent switch- ing between the predominantly vaccinating and non-vaccinating phases of the dynamics.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Impact of network assortativity on epidemic and vaccination","attachmentId":85935719,"attachmentType":"pdf","work_url":"https://www.academia.edu/79098213/Impact_of_network_assortativity_on_epidemic_and_vaccination","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/79098213/Impact_of_network_assortativity_on_epidemic_and_vaccination"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="125359957" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/125359957/Network_topological_determinants_of_pathogen_spread">Network topological determinants of pathogen spread</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="27705029" href="https://ucl.academia.edu/DelmiroFernandezReyes">Delmiro Fernandez-Reyes</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Scientific Reports, 2022</p><p class="ds-related-work--abstract ds2-5-body-sm">Indiscriminate suppression is unsustainable long term and presupposes that all interactions carry equal importance. Instead, transmission within a social network has been shown to be determined by its topology. In this paper, we deploy simulations to understand and quantify the impact on disease transmission of a set of topological network features, building a dataset of 9000 interaction graphs using generators of different types of synthetic social networks. Independently of the topology of the network, we maintain constant the total volume of social interactions in our simulations, to show how even with the same social contact some network structures are more or less resilient to the spread. We find a suitable intervention to be specific suppression of unfamiliar and casual interactions that contribute to the network's global efficiency. This is, pathogen spread is significantly reduced by limiting specific kinds of contact rather than their global number. Our numerical studies might inspire further investigation in connection to public health, as an integrative framework to craft and evaluate social interventions in communicable diseases with different social graphs or as a highlight of network metrics that should be captured in social studies. The contact patterns that underlie disease transmission naturally form a network, where links join individuals that interact, and disease spreads along links. Computational models of infectious disease can support scenario analysis during epidemic outbreaks necessary to devise effective public health interventions. All epidemiological models make assumptions about the underlying network of interactions. Contact network models mathematically formalize this intuitive concept, so that epidemiological calculations explicitly consider complex patterns of interactions 1 . Recent studies 2 have shown that networks with equal number of nodes and edges, but different network structure (e.g. path length and clustering) lead to different infection curves. Most of the theoretical literature on this topic focuses on the effect on pathogen spread of individual network properties (e.g. degree distribution, assortative mixing or clustering), typically analyzed by controlled numerical experiments or analytical calculations, where only the property of interest is varied. However, in a realistic context, altering the structure of a network means simultaneously changing different network characteristics. This is because when one perturbs a network, increasing the variance of the degree distribution, for example, many other network metrics can also change, entangling the effect of different network metrics on spread. Even more, the size and complexity of the space of possible network characteristics makes the derivation of optimal metrics of spread from empirical data infeasible, for any candidate model is bound to be under determined by the scale and fidelity of available data. Rather we need large-scale simulations spanning the horizon of network parameters within which a network topology is bound to lie. Our simulations of the spread of a pathogen using a contact network model on more than 9000 synthetic social networks are a first step in this direction. Although all of the networks considered are synthetic, the families from which they are sampled have been shown to be representative in some instances of human interaction networks. Importantly, the number of social interactions per time step is kept constant for all of our simulations, independently of the network topology and average degree. That is, the same number of social interactions occur on average at each time step of the simulations (i.e., equal to the number of individuals). Note, however, that there are differences across individuals (we assume a linear relationship between the individual average degree and their number of interactions per time step) 9 . Thus, the differences reported across our simulations stem from which individuals in the population interact, rather than the total number of interactions. The analysis of our large-scale simulations demonstrate that metrics that were found to be predictive of the spread in the literature (through experiments that only varied the metric of interest), are not predictive when one considers a larger variety of network topologies. Instead, we show that specific suppression of unfamiliar and casual interactions that contribute to the network's global efficiency is a well suited intervention. Our conclusions</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Network topological determinants of pathogen spread","attachmentId":119418394,"attachmentType":"pdf","work_url":"https://www.academia.edu/125359957/Network_topological_determinants_of_pathogen_spread","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/125359957/Network_topological_determinants_of_pathogen_spread"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="92850426" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/92850426/Immunization_Strategies_for_Networks_with_Scale_Free_Topology">Immunization Strategies for Networks with Scale-Free Topology</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="172572894" href="https://pub.academia.edu/StefanMocanu">Stefan Mocanu</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2006</p><p class="ds-related-work--abstract ds2-5-body-sm">The paper propose a model for complex networks with scale-free degree distribution in which the fraction of sites having k connections follows a power law: P(k)=k-λ. By studying the percolation in such a scale-free model it was established that in the regime 2&lt;λ&lt;3 the networks are resilient to random breakdown. By computing the percolation critical exponents and the resilience to</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Immunization Strategies for Networks with Scale-Free Topology","attachmentId":95749707,"attachmentType":"pdf","work_url":"https://www.academia.edu/92850426/Immunization_Strategies_for_Networks_with_Scale_Free_Topology","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/92850426/Immunization_Strategies_for_Networks_with_Scale_Free_Topology"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":52681954,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":52681954,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_52681954" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="20389445" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/20389445/Effective_vaccination_strategies_for_realistic_social_networks">Effective vaccination strategies for realistic social networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32144300" href="https://tulane.academia.edu/mhyman">James M Hyman</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 2007</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Effective vaccination strategies for realistic social networks","attachmentId":41332961,"attachmentType":"pdf","work_url":"https://www.academia.edu/20389445/Effective_vaccination_strategies_for_realistic_social_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/20389445/Effective_vaccination_strategies_for_realistic_social_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="1" data-entity-id="33205713" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/33205713/Centrality_measures_for_immunization_of_weighted_networks">Centrality measures for immunization of weighted networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="3573924" href="https://iaees.academia.edu/IAEESPublications">IAEES Publications</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Centrality measures for immunization of weighted networks","attachmentId":53285072,"attachmentType":"pdf","work_url":"https://www.academia.edu/33205713/Centrality_measures_for_immunization_of_weighted_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/33205713/Centrality_measures_for_immunization_of_weighted_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="2" data-entity-id="24674268" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/24674268/Imperfect_targeted_immunization_in_scale_free_networks">Imperfect targeted immunization in scale-free networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="47472151" href="https://independent.academia.edu/GaoxiXiao">Gaoxi Xiao</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 2009</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Imperfect targeted immunization in scale-free networks","attachmentId":45004180,"attachmentType":"pdf","work_url":"https://www.academia.edu/24674268/Imperfect_targeted_immunization_in_scale_free_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" 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