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{"title"=>"Epidemic Spread on Weighted Networks", "type"=>"journal", "authors"=>[{"first_name"=>"Christel", "last_name"=>"Kamp", "scopus_author_id"=>"6603747181"}, {"first_name"=>"Mathieu", "last_name"=>"Moslonka-Lefebvre", "scopus_author_id"=>"27967892600"}, {"first_name"=>"Samuel", "last_name"=>"Alizon", "scopus_author_id"=>"16027863300"}], "year"=>2013, "source"=>"PLoS Computational Biology", "identifiers"=>{"issn"=>"1553734X", "scopus"=>"2-s2.0-84892724043", "pui"=>"372170430", "doi"=>"10.1371/journal.pcbi.1003352", "isbn"=>"1553-734X", "sgr"=>"84892724043", "pmid"=>"24348225"}, "id"=>"77c7944a-c34a-33da-9d64-606e2ec87752", "abstract"=>"The contact structure between hosts shapes disease spread. Most network-based models used in epidemiology tend to ignore heterogeneity in the weighting of contacts between two individuals. However, this assumption is known to be at odds with the data for many networks (e.g. sexual contact networks) and to have a critical influence on epidemics' behavior. One of the reasons why models usually ignore heterogeneity in transmission is that we currently lack tools to analyze weighted networks, such that most studies rely on numerical simulations. Here, we present a novel framework to estimate key epidemiological variables, such as the rate of early epidemic expansion (r0) and the basic reproductive ratio (R0), from joint probability distributions of number of partners (contacts) and number of interaction events through which contacts are weighted. These distributions are much easier to infer than the exact shape of the network, which makes the approach widely applicable. The framework also allows for a derivation of the full time course of epidemic prevalence and contact behaviour, which we validate with numerical simulations on networks. Overall, incorporating more realistic contact networks into epidemiological models can improve our understanding of the emergence and spread of infectious diseases.", "link"=>"http://www.mendeley.com/research/epidemic-spread-weighted-networks-1", "reader_count"=>71, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>4, "Researcher"=>19, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>19, "Student > Postgraduate"=>3, "Student > Master"=>10, "Other"=>1, "Student > Bachelor"=>7, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>3, "Professor"=>2}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>4, "Researcher"=>19, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>19, "Student > Postgraduate"=>3, "Student > Master"=>10, "Other"=>1, "Student > Bachelor"=>7, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>3, "Professor"=>2}, "reader_count_by_subject_area"=>{"Unspecified"=>6, "Agricultural and Biological Sciences"=>14, "Veterinary Science and Veterinary Medicine"=>1, "Business, Management and Accounting"=>1, "Chemistry"=>1, "Computer Science"=>8, "Economics, Econometrics and Finance"=>3, "Engineering"=>7, "Environmental Science"=>3, "Materials Science"=>1, "Mathematics"=>12, "Medicine and Dentistry"=>4, "Pharmacology, Toxicology and Pharmaceutical Science"=>1, "Physics and Astronomy"=>4, "Social Sciences"=>3, "Immunology and Microbiology"=>2}, "reader_count_by_subdiscipline"=>{"Materials Science"=>{"Materials Science"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>4}, "Social Sciences"=>{"Social Sciences"=>3}, "Physics and Astronomy"=>{"Physics and Astronomy"=>4}, "Mathematics"=>{"Mathematics"=>12}, "Unspecified"=>{"Unspecified"=>6}, "Environmental Science"=>{"Environmental Science"=>3}, "Pharmacology, Toxicology and Pharmaceutical Science"=>{"Pharmacology, Toxicology and Pharmaceutical Science"=>1}, "Engineering"=>{"Engineering"=>7}, "Chemistry"=>{"Chemistry"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>3}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>14}, "Computer Science"=>{"Computer Science"=>8}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Veterinary Science and Veterinary Medicine"=>{"Veterinary Science and Veterinary Medicine"=>1}}, "reader_count_by_country"=>{"Sweden"=>1, "Iran"=>1, "United States"=>5, "Brazil"=>1, "United Kingdom"=>3, "France"=>1, "Switzerland"=>1, "Portugal"=>1}, "group_count"=>3}

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• {"files"=>["https://ndownloader.figshare.com/files/1312835"], "description"=>"<p><i>β</i> is the transmission probability, <i>γ</i> the recovery rate, the average number of interaction events an individual has, the average number of contacts per individual, is the second moment of the joint probability distribution and is the average number of interaction events per contact. Note that the equation for is exact for .</p>", "links"=>[], "tags"=>["Theoretical biology", "Management engineering", "Management planning and control", "Network analysis (management)", "epidemiology", "Spatial epidemiology", "Sociology", "social networks"], "article_id"=>876077, "categories"=>["Biological Sciences", "Medicine", "Engineering", "Sociology"], "users"=>["Christel Kamp", "Mathieu Moslonka-Lefebvre", "Samuel Alizon"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003352.t002", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_vs_/876077", "title"=>"vs. .", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-12-12 03:23:50"}
• {"files"=>["https://ndownloader.figshare.com/files/1312834"], "description"=>"<p>A) Characteristics of the heterosexual contact network inferred from the NATSAL contact tracing study <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003352#pcbi.1003352-Johnson1\" target=\"_blank\">[28]</a>. The network shows a heterogeneous joint probability distribution , which is the probability for an individual to have <i>k</i> contacts during the last 5 years and <i>l</i> sex acts during the last 4 weeks (higher values of are in red and lower values are in green). This heterogeneity is also seen for the marginal distributions (on the right) and (on the top). B) Dynamics of an SI epidemic spreading on an unweighted (black line) or a weighted sexual contact network. The results of simulations on the weighted network are in grey, the approximations of our model are in red or in orange for the case with assortativity correction. The network has been reduced to nodes with <i>k</i>>0 and transmission probability per sex act is <i>β</i> = 0.01. C) Dynamics of the average number of contacts of susceptible (in green) and infected individuals (in red) over the course of an epidemic spreading on the weighted network. The inset shows the probability of a host to be susceptible or infected at <i>t</i> = 10 years conditioned to the number of contacts during the last 5 years (more or less than 3 contacts). D) Same as panel C but for the number of sex acts . In Panels B, C and D, the weighting is done using the shown in panel A. Individuals with more contacts tend to be disproportionally infected (panel C). Individuals with more sex acts tend to be even more infected (panel D).</p>", "links"=>[], "tags"=>["Theoretical biology", "Management engineering", "Management planning and control", "Network analysis (management)", "epidemiology", "Spatial epidemiology", "Sociology", "social networks", "inferred"], "article_id"=>876076, "categories"=>["Biological Sciences", "Medicine", "Engineering", "Sociology"], "users"=>["Christel Kamp", "Mathieu Moslonka-Lefebvre", "Samuel Alizon"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003352.g003", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Disease_spread_on_a_network_inferred_from_data_/876076", "title"=>"Disease spread on a network inferred from data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-12 03:23:50"}
• {"files"=>["https://ndownloader.figshare.com/files/1312824"], "description"=>"<p>Both the number of contacts that an individual maintains and the weight that (s)he assigns to each contact are relevant for the spread of an infectious agent. Here, each individual has <i>l</i> interaction events that (s)he can distribute among his/her <i>k</i> contacts. On the scale of the transmission network, these are modelled by the joint probability distribution to find an individual with <i>k</i> contacts and <i>l</i> interaction events per time interval.</p>", "links"=>[], "tags"=>["Theoretical biology", "Management engineering", "Management planning and control", "Network analysis (management)", "epidemiology", "Spatial epidemiology", "Sociology", "social networks"], "article_id"=>876066, "categories"=>["Biological Sciences", "Medicine", "Engineering", "Sociology"], "users"=>["Christel Kamp", "Mathieu Moslonka-Lefebvre", "Samuel Alizon"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003352.g001", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Weighting_between_contacts_/876066", "title"=>"Weighting between contacts.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-12 03:23:50"}
• {"files"=>["https://ndownloader.figshare.com/files/1312837", "https://ndownloader.figshare.com/files/1312838", "https://ndownloader.figshare.com/files/1312839", "https://ndownloader.figshare.com/files/1312840", "https://ndownloader.figshare.com/files/1312841", "https://ndownloader.figshare.com/files/1312842"], "description"=>"<div><p>The contact structure between hosts shapes disease spread. Most network-based models used in epidemiology tend to ignore heterogeneity in the weighting of contacts between two individuals. However, this assumption is known to be at odds with the data for many networks (e.g. sexual contact networks) and to have a critical influence on epidemics' behavior. One of the reasons why models usually ignore heterogeneity in transmission is that we currently lack tools to analyze weighted networks, such that most studies rely on numerical simulations. Here, we present a novel framework to estimate key epidemiological variables, such as the rate of early epidemic expansion () and the basic reproductive ratio (), from joint probability distributions of number of partners (contacts) and number of interaction events through which contacts are weighted. These distributions are much easier to infer than the exact shape of the network, which makes the approach widely applicable. The framework also allows for a derivation of the full time course of epidemic prevalence and contact behaviour, which we validate with numerical simulations on networks. Overall, incorporating more realistic contact networks into epidemiological models can improve our understanding of the emergence and spread of infectious diseases.</p></div>", "links"=>[], "tags"=>["Theoretical biology", "Management engineering", "Management planning and control", "Network analysis (management)", "epidemiology", "Spatial epidemiology", "Sociology", "social networks", "weighted"], "article_id"=>876079, "categories"=>["Biological Sciences", "Medicine", "Engineering", "Sociology"], "users"=>["Christel Kamp", "Mathieu Moslonka-Lefebvre", "Samuel Alizon"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003352.s001", "https://dx.doi.org/10.1371/journal.pcbi.1003352.s002", "https://dx.doi.org/10.1371/journal.pcbi.1003352.s003", "https://dx.doi.org/10.1371/journal.pcbi.1003352.s004", "https://dx.doi.org/10.1371/journal.pcbi.1003352.s005", "https://dx.doi.org/10.1371/journal.pcbi.1003352.s006"], "stats"=>{"downloads"=>13, "page_views"=>29, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Epidemic_Spread_on_Weighted_Networks_/876079", "title"=>"Epidemic Spread on Weighted Networks", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-12-12 03:23:50"}
• {"files"=>["https://ndownloader.figshare.com/files/1312836"], "description"=>"<p><i>A</i>,<i>B</i> correspond to epidemic stages, i.e. <i>S</i>, <i>I</i>, <i>R</i> for susceptible, infected, recovered.</p>", "links"=>[], "tags"=>["Theoretical biology", "Management engineering", "Management planning and control", "Network analysis (management)", "epidemiology", "Spatial epidemiology", "Sociology", "social networks"], "article_id"=>876078, "categories"=>["Biological Sciences", "Medicine", "Engineering", "Sociology"], "users"=>["Christel Kamp", "Mathieu Moslonka-Lefebvre", "Samuel Alizon"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003352.t001", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Notations_used_in_the_study_/876078", "title"=>"Notations used in the study.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-12-12 03:23:50"}
• {"files"=>["https://ndownloader.figshare.com/files/1312826"], "description"=>"<p>The distributions in the number of contacts (<i>k</i>) and interaction events per time (<i>l</i>) are either homogeneous (Poisson) or heterogeneous (power law). For the number of interaction events, we also show the linear case in which <i>l</i> is strictly proportional to the number of contacts <i>k</i>, i.e. . <i>k</i> and <i>l</i> are drawn from joint distributions with (except for the analytical model's linear case where being compensated by a double transmission rate). The figures show the epidemic prevalence <i>I</i> as the outcome of the simulation runs (grey, dotted lines), of the the numerical solution of the analytical model with (red, solid line) and (red, dashed line). In addition, we show the epidemic prevalence when excluding individuals with only one contact () which is relevant for epidemics on networks with heterogeneous numbers of contacts including many individuals with in combination with a (nearly) constant number of interaction events, as realised through a Poisson distribution (orange line, cf. specifically power law, Poisson). Parameters chosen correspond to (Poisson case: , , power law case: , , ). Epidemiological parameters are <i>β</i> = 0.01 (0.02 for the analytical model's linear case), <i>γ</i> = 0.004 in arbitrary units and <i>I</i>(0) = 20. The insets show the same data for the early epidemic expansion in logarithmic scale showing early exponential growth according to (black line) with from <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003352#pcbi-1003352-t002\" target=\"_blank\">Table 2</a>.</p>", "links"=>[], "tags"=>["Theoretical biology", "Management engineering", "Management planning and control", "Network analysis (management)", "epidemiology", "Spatial epidemiology", "Sociology", "social networks", "infected", "hosts", "spreading", "types"], "article_id"=>876068, "categories"=>["Biological Sciences", "Medicine", "Engineering", "Sociology"], "users"=>["Christel Kamp", "Mathieu Moslonka-Lefebvre", "Samuel Alizon"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003352.g002", "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dynamics_of_the_number_of_infected_hosts_I_during_epidemic_spreading_on_different_types_of_networks_/876068", "title"=>"Dynamics of the number of infected hosts (<i>I</i>) during epidemic spreading on different types of networks.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-12 03:23:50"}

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• {"unique-ip"=>"5", "full-text"=>"5", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"9"}
• {"unique-ip"=>"14", "full-text"=>"15", "pdf"=>"4", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"10"}
• {"unique-ip"=>"2", "full-text"=>"0", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"12"}

Relative Metric

{"start_date"=>"2013-01-01T00:00:00Z", "end_date"=>"2013-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Computer and information sciences", "average_usage"=>[297, 488, 616, 724, 828, 939, 1038, 1127, 1223, 1311, 1393, 1479, 1556]}, {"subject_area"=>"/Computer and information sciences/Network analysis", "average_usage"=>[340, 548, 701, 844, 945, 1073, 1189, 1282, 1391, 1488, 1562, 1660, 1731]}, {"subject_area"=>"/Medicine and health sciences/Pathology and laboratory medicine", "average_usage"=>[267, 466, 592, 709, 806, 901, 989, 1075, 1162, 1254, 1342, 1424, 1486]}, {"subject_area"=>"/Physical sciences/Mathematics", "average_usage"=>[259, 431, 541, 639, 727, 816, 898, 980, 1061, 1136, 1214, 1294, 1356]}]}

F1000Prime