Towards a Characterization of Behavior-Disease Models
Publication Date
August 03, 2011
Journal
PLOS ONE
Authors
Nicola Perra, Duygu Balcan, Bruno Gonçalves & Alessandro Vespignani
Volume
6
Issue
8
Pages
e23084
DOI
https://dx.plos.org/10.1371/journal.pone.0023084
Publisher URL
http://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0023084
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/21826228
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3149628
Europe PMC
http://europepmc.org/abstract/MED/21826228
Web of Science
000293558900054
Scopus
79961051637
Mendeley
http://www.mendeley.com/research/towards-characterization-behaviordisease-models
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Mendeley | Further Information

{"title"=>"Towards a characterization of behavior-disease models", "type"=>"journal", "authors"=>[{"first_name"=>"Nicola", "last_name"=>"Perra", "scopus_author_id"=>"24824755600"}, {"first_name"=>"Duygu", "last_name"=>"Balcan", "scopus_author_id"=>"6506594355"}, {"first_name"=>"Bruno", "last_name"=>"Gonçalves", "scopus_author_id"=>"55392410900"}, {"first_name"=>"Alessandro", "last_name"=>"Vespignani", "scopus_author_id"=>"7004546582"}], "year"=>2011, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "pui"=>"362270523", "doi"=>"10.1371/journal.pone.0023084", "sgr"=>"79961051637", "arxiv"=>"1107.0997", "scopus"=>"2-s2.0-79961051637", "isbn"=>"1932-6203", "pmid"=>"21826228"}, "id"=>"a520b648-1eae-3aec-b9b9-f49fd50902b6", "abstract"=>"The last decade saw the advent of increasingly realistic epidemic models that leverage on the availability of highly detailed census and human mobility data. Data-driven models aim at a granularity down to the level of households or single individuals. However, relatively little systematic work has been done to provide coupled behavior-disease models able to close the feedback loop between behavioral changes triggered in the population by an individual's perception of the disease spread and the actual disease spread itself. While models lacking this coupling can be extremely successful in mild epidemics, they obviously will be of limited use in situations where social disruption or behavioral alterations are induced in the population by knowledge of the disease. Here we propose a characterization of a set of prototypical mechanisms for self-initiated social distancing induced by local and non-local prevalence-based information available to individuals in the population. We characterize the effects of these mechanisms in the framework of a compartmental scheme that enlarges the basic SIR model by considering separate behavioral classes within the population. The transition of individuals in/out of behavioral classes is coupled with the spreading of the disease and provides a rich phase space with multiple epidemic peaks and tipping points. The class of models presented here can be used in the case of data-driven computational approaches to analyze scenarios of social adaptation and behavioral change.", "link"=>"http://www.mendeley.com/research/towards-characterization-behaviordisease-models", "reader_count"=>68, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>9, "Researcher"=>13, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>23, "Student > Master"=>6, "Other"=>1, "Student > Bachelor"=>3, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>1, "Professor"=>9}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>9, "Researcher"=>13, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>23, "Student > Master"=>6, "Other"=>1, "Student > Bachelor"=>3, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>1, "Professor"=>9}, "reader_count_by_subject_area"=>{"Engineering"=>4, "Unspecified"=>5, "Mathematics"=>11, "Agricultural and Biological Sciences"=>7, "Medicine and Dentistry"=>6, "Neuroscience"=>1, "Business, Management and Accounting"=>1, "Physics and Astronomy"=>17, "Psychology"=>2, "Social Sciences"=>3, "Computer Science"=>10, "Economics, Econometrics and Finance"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>4}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>6}, "Neuroscience"=>{"Neuroscience"=>1}, "Social Sciences"=>{"Social Sciences"=>3}, "Physics and Astronomy"=>{"Physics and Astronomy"=>17}, "Psychology"=>{"Psychology"=>2}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>7}, "Computer Science"=>{"Computer Science"=>10}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Mathematics"=>{"Mathematics"=>11}, "Unspecified"=>{"Unspecified"=>5}}, "reader_count_by_country"=>{"Belgium"=>1, "United States"=>2, "Brazil"=>1, "Italy"=>3, "France"=>1, "Australia"=>1, "Spain"=>2, "India"=>1}, "group_count"=>2}

CrossRef

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/749753"], "description"=>"<p>We compare the solution of the deterministic equations (red solid line) with the reference ranges of our stochastic solutions. Here we consider runs that produced at least an epidemic size of of the population ().</p>", "links"=>[], "tags"=>["fixing"], "article_id"=>420128, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g005", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_I_fixing__and_/420128", "title"=>"Model I fixing , , and .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:05:01"}
  • {"files"=>["https://ndownloader.figshare.com/files/749430"], "description"=>"<p>Model I Schematic representation of Model I.</p>", "links"=>[], "tags"=>["schematic"], "article_id"=>419806, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g003", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_I_Schematic_representation_of_Model_I_/419806", "title"=>"Model I Schematic representation of Model I.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:03:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/750614"], "description"=>"<p> Fixing , , , , and . The three lines are curves of as a function of , keeping constant. We select three different values of which correspond to solid black, red, and dashed lines, respectively. The value is a special case that leads to . It divides the phase space in two different regions. All the values of below are characterized by . In this case for large values of the model is reduced to an SIR with reproductive number below and the epidemic is halted. Interestingly, this behavior starts in an intermediate regime of . There is a critical value of above which (i.e., ) the epidemic size is zero. This transition happens with a jump, as shown by the solid black line. All the values of above are instead characterized by . Also in this case the model is reduced to an SIR with reproductive number for large values of , but in this case this value is above . This results in a epidemic size that is always non-zero. In this region of parameters no jumps are present (see the dashed line). The values shown in the plot are computed through numerical integration of the equations.</p>", "links"=>[], "tags"=>["iii"], "article_id"=>420987, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g014", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_III_Reduction_of_the_epidemic_size_as_a_function_of_and_/420987", "title"=>"Model III Reduction of the epidemic size as a function of and .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:09:40"}
  • {"files"=>["https://ndownloader.figshare.com/files/750118"], "description"=>"<p>The pseudo mass-action law is represented by the dashed line.</p>", "links"=>[], "tags"=>["ii", "schematic"], "article_id"=>420490, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g009", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_II_Schematic_representation_of_Model_II_/420490", "title"=>"Model II Schematic representation of Model II.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:06:59"}
  • {"files"=>["https://ndownloader.figshare.com/files/750503"], "description"=>"<p>We display the regions of parameter space on - plane exhibiting different number of disease activity peaks for three different values of , where we have fixed , , and . The phase diagram has been obtained by numerical integration of the deterministic equations in Eq. (30).</p>", "links"=>[], "tags"=>["iii", "diagram", "waves"], "article_id"=>420873, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g013", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_III_Phase_diagram_of_infection_waves_on_plane_/420873", "title"=>"Model III Phase diagram of infection waves on - plane.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:09:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/749250"], "description"=>"<p>In panel (A) we show the first in which individuals in compartment interact with individuals in class , represented by the small square, becoming themselves. In general the compartment inducing the transition of individuals in could be any other compartment in the model, e.g. , different from the end-point of the transition. We assume the homogeneous mixing of the population so that the rate at which an individual in interacts with individuals in and changes status is simply given by the product of prevalence of and the transmission rate , . This type of reaction can be written as . In the case of the SIR model and . In panel (B) we show the second type. This is a spontaneous transition with rate in which an individual in compartment spontaneously moves to compartment . These types of reactions can be written as . In the SIR model and .</p>", "links"=>[], "tags"=>["types", "transitions", "recurrent"], "article_id"=>419624, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g001", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_representation_of_the_two_types_of_transitions_that_will_be_recurrent_in_the_paper_/419624", "title"=>"Schematic representation of the two types of transitions that will be recurrent in the paper.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:02:20"}
  • {"files"=>["https://ndownloader.figshare.com/files/750917"], "description"=>"<p>In the last column we write the model in which the transition has been used. For example, the first transition is related to the disease dynamic and has been used in all three models.</p>", "links"=>[], "tags"=>["transitions", "rates"], "article_id"=>421291, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.t001", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_In_this_table_we_show_all_the_transitions_and_their_rates_used_in_the_three_different_models_/421291", "title"=>"In this table we show all the transitions and their rates used in the three different models.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-20 16:11:17"}
  • {"files"=>["https://ndownloader.figshare.com/files/749527"], "description"=>"<p>We show the medians of , evaluated using stochastic runs for the baseline (SIR model without fear of contagion) and three realizations of the model for different values of . In particular in panel (A) we show the baseline SIR model with the same disease parameters. In panel (B) we set . In panel (C) we set . In panel (D) we set . It is clear how the peak time is the same for all the scenarios and how the number of infected individuals at peak is reduced as increases.</p>", "links"=>[], "tags"=>["Computational biology", "physics", "mathematics"], "article_id"=>419900, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g004", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_I_for__and_/419900", "title"=>"Model I for , , , and .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:03:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/749851"], "description"=>"<p>Fixing , , , , and we show stochastic runs of the infected profiles and the median evaluated considering runs in which the epidemic size is at least of the population.</p>", "links"=>[], "tags"=>["waves"], "article_id"=>420226, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g006", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_I_Multiple_waves_of_infection_/420226", "title"=>"Model I Multiple waves of infection.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:05:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/750410"], "description"=>"<p>Fixing , , , , and we show stochastic runs and the medians evaluated considering runs for two different values of . In panel (A) . In panel (B) .</p>", "links"=>[], "tags"=>["iii", "waves"], "article_id"=>420782, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g012", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_III_Multiple_waves_of_infection_/420782", "title"=>"Model III Multiple waves of infection.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:08:36"}
  • {"files"=>["https://ndownloader.figshare.com/files/749369"], "description"=>"<p>In this case the transition into compartment is based on the absolute number of the individuals in the compartment (shown by the small square). In general the inducing compartment could be different (e.g. ) than the end-point of the transition.</p>", "links"=>[], "tags"=>["Computational biology", "physics", "mathematics"], "article_id"=>419739, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g002", "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_representation_of_the_third_type_of_interaction_discussed_/419739", "title"=>"Schematic representation of the third type of interaction discussed.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:02:59"}
  • {"files"=>["https://ndownloader.figshare.com/files/749925"], "description"=>"<p> We display the regions of parameter space on - plane exhibiting different number of disease activity peaks for three different values of , where we have fixed , and . The phase diagram has been obtained by numerical integration of the deterministic equations in Eq. (12).</p>", "links"=>[], "tags"=>["diagram", "waves"], "article_id"=>420300, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g007", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_I_Phase_diagram_of_infection_waves_on_plane_/420300", "title"=>"Model I Phase diagram of infection waves on - plane.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:05:56"}
  • {"files"=>["https://ndownloader.figshare.com/files/750852"], "description"=>"<p>The values are obtained by numerical integration of the equations.</p>", "links"=>[], "tags"=>["iii"], "article_id"=>421226, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g015", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_III_and_for__and_/421226", "title"=>"Model III and for , , , , , and .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:10:54"}
  • {"files"=>["https://ndownloader.figshare.com/files/750010"], "description"=>"<p>Once the product is smaller than unity, then the epidemic size goes to as .</p>", "links"=>[], "tags"=>["fixing", "normalized"], "article_id"=>420389, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g008", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_I_fixing__and_we_evaluate_the_normalized_epidemic_size_for_different_values_of_and_through_direct_integration_of_the_equations_/420389", "title"=>"Model I fixing , , and we evaluate the normalized epidemic size for different values of and through direct integration of the equations.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:06:25"}
  • {"files"=>["https://ndownloader.figshare.com/files/750321"], "description"=>"<p>Model III Schematic representation of Model III.</p>", "links"=>[], "tags"=>["iii", "schematic"], "article_id"=>420694, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g011", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_III_Schematic_representation_of_Model_III_/420694", "title"=>"Model III Schematic representation of Model III.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:08:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/750206"], "description"=>"<p>We fix , , and . In panel (A) we assume for which . Increasing the value of results in an asymptotic value of the epidemic size other than zero. In panel (B) we consider . In this case, instead, . By increasing the value of the epidemic size is increasingly reduced. This effect is stronger for bigger values of . The values are obtained by numerical integration of the equations.</p>", "links"=>[], "tags"=>["ii"], "article_id"=>420577, "categories"=>["Physics", "Mathematics", "Biological Sciences"], "users"=>["Nicola Perra", "Duygu Balcan", "Bruno Gonçalves", "Alessandro Vespignani"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0023084.g010", "stats"=>{"downloads"=>3, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_II_Reduction_of_the_epidemic_size_as_a_function_of_for_different_values_of_and_/420577", "title"=>"Model II Reduction of the epidemic size as a function of for different values of and .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-20 16:07:27"}

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Relative Metric

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