Untangling the Interplay between Epidemic Spread and Transmission Network Dynamics
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{"title"=>"Untangling the interplay between epidemic spread and transmission network dynamics", "type"=>"journal", "authors"=>[{"first_name"=>"Christel", "last_name"=>"Kamp", "scopus_author_id"=>"6603747181"}], "year"=>2010, "source"=>"PLoS Computational Biology", "identifiers"=>{"arxiv"=>"arXiv:0912.4189v1", "sgr"=>"78649648877", "pmid"=>"21124951", "isbn"=>"1553-7358 (Electronic)\\r1553-734X (Linking)", "pui"=>"360077017", "issn"=>"1553734X", "scopus"=>"2-s2.0-78649648877", "doi"=>"10.1371/journal.pcbi.1000984"}, "id"=>"bbc8f5f3-c273-3152-b416-59a24a851b9c", "abstract"=>"The epidemic spread of infectious diseases is ubiquitous and often has a considerable impact on public health and economic wealth. The large variability in the spatio-temporal patterns of epidemics prohibits simple interventions and requires a detailed analysis of each epidemic with respect to its infectious agent and the corresponding routes of transmission. To facilitate this analysis, we introduce a mathematical framework which links epidemic patterns to the topology and dynamics of the underlying transmission network. The evolution, both in disease prevalence and transmission network topology, is derived from a closed set of partial differential equations for infections without allowing for recovery. The predictions are in excellent agreement with complementarily conducted agent-based simulations. The capacity of this new method is demonstrated in several case studies on HIV epidemics in synthetic populations: it allows us to monitor the evolution of contact behavior among healthy and infected individuals and the contributions of different disease stages to the spreading of the epidemic. This gives both direction to and a test bed for targeted intervention strategies for epidemic control. In conclusion, this mathematical framework provides a capable toolbox for the analysis of epidemics from first principles. This allows for fast, in silico modeling--and manipulation--of epidemics and is especially powerful if complemented with adequate empirical data for parameterization.", "link"=>"http://www.mendeley.com/research/untangling-interplay-between-epidemic-spread-transmission-network-dynamics", "reader_count"=>103, "reader_count_by_academic_status"=>{"Unspecified"=>2, "Professor > Associate Professor"=>8, "Researcher"=>31, "Student > Doctoral Student"=>3, "Student > Ph. D. Student"=>35, "Student > Postgraduate"=>2, "Student > Master"=>5, "Other"=>3, "Student > Bachelor"=>4, "Lecturer > Senior Lecturer"=>4, "Professor"=>6}, "reader_count_by_user_role"=>{"Unspecified"=>2, "Professor > Associate Professor"=>8, "Researcher"=>31, "Student > Doctoral Student"=>3, "Student > Ph. D. Student"=>35, "Student > Postgraduate"=>2, "Student > Master"=>5, "Other"=>3, "Student > Bachelor"=>4, "Lecturer > Senior Lecturer"=>4, "Professor"=>6}, "reader_count_by_subject_area"=>{"Unspecified"=>13, "Agricultural and Biological Sciences"=>16, "Veterinary Science and Veterinary Medicine"=>2, "Business, Management and Accounting"=>1, "Computer Science"=>11, "Economics, Econometrics and Finance"=>1, "Engineering"=>5, "Environmental Science"=>2, "Biochemistry, Genetics and Molecular Biology"=>1, "Mathematics"=>16, "Medicine and Dentistry"=>19, "Physics and Astronomy"=>10, "Social Sciences"=>5, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>19}, "Social Sciences"=>{"Social Sciences"=>5}, "Physics and Astronomy"=>{"Physics and Astronomy"=>10}, "Mathematics"=>{"Mathematics"=>16}, "Unspecified"=>{"Unspecified"=>13}, "Environmental Science"=>{"Environmental Science"=>2}, "Engineering"=>{"Engineering"=>5}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>16}, "Computer Science"=>{"Computer Science"=>11}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Veterinary Science and Veterinary Medicine"=>{"Veterinary Science and Veterinary Medicine"=>2}}, "reader_count_by_country"=>{"Canada"=>1, "United States"=>6, "United Kingdom"=>8, "Italy"=>2, "Israel"=>1, "Australia"=>1, "Switzerland"=>1, "Portugal"=>1, "Germany"=>2, "Spain"=>1}, "group_count"=>10}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/407557"], "description"=>"<div><p>The epidemic spread of infectious diseases is ubiquitous and often has a considerable impact on public health and economic wealth. The large variability in the spatio-temporal patterns of epidemics prohibits simple interventions and requires a detailed analysis of each epidemic with respect to its infectious agent and the corresponding routes of transmission. To facilitate this analysis, we introduce a mathematical framework which links epidemic patterns to the topology and dynamics of the underlying transmission network. The evolution, both in disease prevalence and transmission network topology, is derived from a closed set of partial differential equations for infections without allowing for recovery. The predictions are in excellent agreement with complementarily conducted agent-based simulations. The capacity of this new method is demonstrated in several case studies on HIV epidemics in synthetic populations: it allows us to monitor the evolution of contact behavior among healthy and infected individuals and the contributions of different disease stages to the spreading of the epidemic. This gives both direction to and a test bed for targeted intervention strategies for epidemic control. In conclusion, this mathematical framework provides a capable toolbox for the analysis of epidemics from first principles. This allows for fast, <em>in silico</em> modeling - and manipulation - of epidemics and is especially powerful if complemented with adequate empirical data for parameterization.</p> </div>", "links"=>[], "tags"=>["untangling", "interplay"], "article_id"=>140507, "categories"=>["Evolutionary Biology", "Biological Sciences", "Neuroscience", "Mathematics", "Cancer", "Medicine", "Physics", "Biophysics"], "users"=>["Christel Kamp"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000984"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Untangling_the_Interplay_between_Epidemic_Spread_and_Transmission_Network_Dynamics/140507", "title"=>"Untangling the Interplay between Epidemic Spread and Transmission Network Dynamics", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2010-11-18 00:08:27"}
  • {"files"=>["https://ndownloader.figshare.com/files/817524"], "description"=>"<p>The dotted, light colored curves correspond to the result of 100 agent-based simulations; the solid lines are the results of the numerical solution of the set of partial differential equations (1–6), parameters are chosen analogous to <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000984#pcbi.1000984-Volz1\" target=\"_blank\">[19]</a>, average number of contacts  = 3, transmission rate of  = 0.2, recovery rate of  = 0.1. Epidemics in networks with differences in the heterogeneity and transience of contacts are shown. The first column shows a static Poisson network with a degree distribution of , as opposed to a network with a scale free degree distribution, , in column 2 (same average degree). Column 3 corresponds to the network in column 1 with an additional demographic process (birth and death at a rate of ). Column 4 corresponds to column 1 with the additional feature that contact partners change at a rate  = 0.2. Epidemics are initiated with 10 infected individuals in an otherwise susceptible population (i.e.  = 10,  = 9990). Links between susceptible and infected hosts, as well as their contact behavior, are initially uncorrelated, i.e., .</p>", "links"=>[], "tags"=>["numbers", "susceptible", "infected", "individuals", "contacts"], "article_id"=>487891, "categories"=>["Evolutionary Biology", "Computational Biology", "Neuroscience", "Mathematics", "Infectious Diseases", "Medicine", "Physics", "Biophysics"], "users"=>["Christel Kamp"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000984.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_the_numbers_of_susceptible_green_and_infected_red_individuals_top_panel_as_well_as_their_average_number_of_contacts_per_person_bottom_panel_/487891", "title"=>"Evolution of the numbers of susceptible (green) and infected (red) individuals (top panel) as well as their average number of contacts per person (bottom panel).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-11-18 02:11:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/817613"], "description"=>"<p>Evolution in the numbers of susceptible, primarily and latently infected individuals is shown in panel A, their average number of contacts per person during the epidemic is presented in panel B. The dotted, light colored curves correspond to the results of 20 agent-based simulations. The solid lines are the result of the numerical solution of the set of partial differential equations. A logarithmic scale was chosen to present the different orders of magnitude in the size of the epidemic subgroups. The epidemics take place on a scale free network with an average degree  = 1.6 into which individuals are born at a rate of  = 0.02 p.a. and die at a rate of  = 0.015 p.a.. The epidemic parameters are chosen in accordance with the infectious profile of HIV <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000984#pcbi.1000984-Hollingsworth1\" target=\"_blank\">[33]</a>, i.e., transmission rates in the stages of primary and latent infection are  = 2.76 p.a. and  = 0.1 p.a., respectively, with rates of progression of  = 4.1 p.a. and  = 0.12 p.a.. Epidemics are initiated with 10 infected individuals in an otherwise susceptible population (i.e.,  = 9,  = 1,  = 9990). Links between susceptible and infected hosts, as well as their contact behavior, are initially uncorrelated, i.e. , . Panels C and D show the evolution of the probability generating functions and distributions in the number of contacts over 20 years of the epidemic for individuals newly entering the population (, ) as well as in susceptible, primarily and latently infected individuals (, , ). The contour plots of the PGFs interpolate from 0 (dark colors) to 1 (light colors) in steps of 0.1.</p>", "links"=>[], "tags"=>["numbers", "susceptible", "latently", "infected", "individuals"], "article_id"=>487980, "categories"=>["Evolutionary Biology", "Computational Biology", "Neuroscience", "Mathematics", "Infectious Diseases", "Medicine", "Physics", "Biophysics"], "users"=>["Christel Kamp"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000984.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_in_the_numbers_of_susceptible_green_primarily_red_and_latently_orange_infected_individuals_as_well_as_in_their_contact_behavior_/487980", "title"=>"Evolution in the numbers of susceptible (green), primarily (red) and latently (orange) infected individuals as well as in their contact behavior.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-11-18 02:13:00"}
  • {"files"=>["https://ndownloader.figshare.com/files/817702"], "description"=>"<p>Evolution in the numbers of susceptible (green), primarily (red) and latently (orange) infected individuals as well as their average number of contacts per person in the scenario of strong and weak concurrency are shown in the left and middle column. The logarithmic scale was chosen to present the different orders of magnitude in the size of the epidemic subgroups. The epidemics take place on random networks with the sketched distributions in the number of contacts ( to are shown,  = 0 for ) into which individuals are born and die at a rate of p.a.. The epidemic parameters were chosen in accordance with the infectious profile of HIV <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000984#pcbi.1000984-Hollingsworth1\" target=\"_blank\">[33]</a>, i.e., transmission rates in the stages of primary and latent infection are p.a. and p.a., respectively, with rates of progression of  = 4.1 p.a. and  = 0.12 p.a.. The right column (comparison, top) shows the fraction of individuals in the primary (red) and latent (orange) stage of disease in the scenarios of strong concurrency (solid lines) and weak concurrency (dashed lines), for comparison. The final diagram shows the ratio, , for both scenarios, i.e. the relative risk of infection acquired from primary over that from latent infections (strong concurrency - solid line, weak concurrency - dashed line). Epidemics are initiated as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000984#pcbi-1000984-g002\" target=\"_blank\">Fig. 2</a>, for better comparability the time axis was shifted to start both epidemics with the same number of latent cases after initial equilibration.</p>", "links"=>[], "tags"=>["epidemics", "synthetic", "populations"], "article_id"=>488074, "categories"=>["Evolutionary Biology", "Computational Biology", "Neuroscience", "Mathematics", "Infectious Diseases", "Medicine", "Physics", "Biophysics"], "users"=>["Christel Kamp"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000984.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_HIV_epidemics_in_synthetic_populations_with_weak_and_strong_concurrency_/488074", "title"=>"HIV epidemics in synthetic populations with weak and strong concurrency.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-11-18 02:14:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/817774"], "description"=>"<p>Note, that , correspond to the stages that are passed during an infection, e.g. for susceptible, for infected etc. Throughout the manuscript derivatives with respect to time/spatial variables are denoted by a dot/prime.</p>", "links"=>[], "tags"=>["parameters"], "article_id"=>488150, "categories"=>["Evolutionary Biology", "Computational Biology", "Neuroscience", "Mathematics", "Infectious Diseases", "Medicine", "Physics", "Biophysics"], "users"=>["Christel Kamp"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1000984.t001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Notation_and_parameters_of_the_model_/488150", "title"=>"Notation and parameters of the model.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2010-11-18 02:15:50"}

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Relative Metric

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