Coupled Contagion Dynamics of Fear and Disease: Mathematical and Computational Explorations
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{"title"=>"Coupled contagion dynamics of fear and disease: Mathematical and computational explorations", "type"=>"journal", "authors"=>[{"first_name"=>"Joshua M.", "last_name"=>"Epstein", "scopus_author_id"=>"55697274700"}, {"first_name"=>"Jon", "last_name"=>"Parker", "scopus_author_id"=>"7404596448"}, {"first_name"=>"Derek", "last_name"=>"Cummings", "scopus_author_id"=>"9842706300"}, {"first_name"=>"Ross A.", "last_name"=>"Hammond", "scopus_author_id"=>"7202457156"}], "year"=>2008, "source"=>"PLoS ONE", "identifiers"=>{"pui"=>"354011718", "sgr"=>"58049191447", "issn"=>"19326203", "pmid"=>"19079607", "scopus"=>"2-s2.0-58049191447", "doi"=>"10.1371/journal.pone.0003955", "isbn"=>"1932-6203; 1932-6203"}, "id"=>"f39304a5-fa3b-372b-bb96-24d2dbfa404f", "abstract"=>"BACKGROUND: In classical mathematical epidemiology, individuals do not adapt their contact behavior during epidemics. They do not endogenously engage, for example, in social distancing based on fear. Yet, adaptive behavior is well-documented in true epidemics. We explore the effect of including such behavior in models of epidemic dynamics.\\n\\nMETHODOLOGY/PRINCIPAL FINDINGS: Using both nonlinear dynamical systems and agent-based computation, we model two interacting contagion processes: one of disease and one of fear of the disease. Individuals can \"contract\" fear through contact with individuals who are infected with the disease (the sick), infected with fear only (the scared), and infected with both fear and disease (the sick and scared). Scared individuals--whether sick or not--may remove themselves from circulation with some probability, which affects the contact dynamic, and thus the disease epidemic proper. If we allow individuals to recover from fear and return to circulation, the coupled dynamics become quite rich, and can include multiple waves of infection. We also study flight as a behavioral response.\\n\\nCONCLUSIONS/SIGNIFICANCE: In a spatially extended setting, even relatively small levels of fear-inspired flight can have a dramatic impact on spatio-temporal epidemic dynamics. Self-isolation and spatial flight are only two of many possible actions that fear-infected individuals may take. Our main point is that behavioral adaptation of some sort must be considered.", "link"=>"http://www.mendeley.com/research/coupled-contagion-dynamics-fear-disease-mathematical-computational-explorations", "reader_count"=>146, "reader_count_by_academic_status"=>{"Unspecified"=>6, "Professor > Associate Professor"=>14, "Librarian"=>1, "Researcher"=>36, "Student > Doctoral Student"=>6, "Student > Ph. D. Student"=>45, "Student > Postgraduate"=>4, "Student > Master"=>14, "Other"=>3, "Student > Bachelor"=>7, "Lecturer > Senior Lecturer"=>1, "Professor"=>9}, "reader_count_by_user_role"=>{"Unspecified"=>6, "Professor > Associate Professor"=>14, "Librarian"=>1, "Researcher"=>36, "Student > Doctoral Student"=>6, "Student > Ph. D. Student"=>45, "Student > Postgraduate"=>4, "Student > Master"=>14, "Other"=>3, "Student > Bachelor"=>7, "Lecturer > Senior Lecturer"=>1, "Professor"=>9}, "reader_count_by_subject_area"=>{"Unspecified"=>13, "Agricultural and Biological Sciences"=>20, "Arts and Humanities"=>2, "Philosophy"=>2, "Business, Management and Accounting"=>4, "Computer Science"=>19, "Decision Sciences"=>1, "Economics, Econometrics and Finance"=>3, "Engineering"=>14, "Environmental Science"=>10, "Biochemistry, Genetics and Molecular Biology"=>1, "Mathematics"=>15, "Medicine and Dentistry"=>11, "Design"=>1, "Neuroscience"=>3, "Physics and Astronomy"=>6, "Psychology"=>3, "Social Sciences"=>17, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>11}, "Social Sciences"=>{"Social Sciences"=>17}, "Decision Sciences"=>{"Decision Sciences"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>6}, "Psychology"=>{"Psychology"=>3}, "Mathematics"=>{"Mathematics"=>15}, "Unspecified"=>{"Unspecified"=>13}, "Environmental Science"=>{"Environmental Science"=>10}, "Arts and Humanities"=>{"Arts and Humanities"=>2}, "Design"=>{"Design"=>1}, "Engineering"=>{"Engineering"=>14}, "Neuroscience"=>{"Neuroscience"=>3}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>3}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>20}, "Computer Science"=>{"Computer Science"=>19}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>4}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Philosophy"=>{"Philosophy"=>2}}, "reader_count_by_country"=>{"United States"=>16, "United Kingdom"=>4, "Zambia"=>1, "Portugal"=>1, "Spain"=>1, "Canada"=>1, "Austria"=>1, "Saint Lucia"=>1, "Belgium"=>1, "Italy"=>1, "Mexico"=>2, "Israel"=>1, "Australia"=>1, "France"=>1, "Germany"=>1}, "group_count"=>7}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/914420"], "description"=>"<p>Transmission Probabilities.</p>", "links"=>[], "tags"=>["Computational biology", "Infectious diseases", "mathematics/nonlinear dynamics"], "article_id"=>584880, "categories"=>["Mathematics", "Biological Sciences", "Infectious Diseases"], "users"=>["Joshua M. Epstein", "Jon Parker", "Derek Cummings", "Ross A. Hammond"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003955.t001", "stats"=>{"downloads"=>3, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Transmission_Probabilities_/584880", "title"=>"Transmission Probabilities.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 07:27:18"}
  • {"files"=>["https://ndownloader.figshare.com/files/913803"], "description"=>"<p>Emboldened by the falling disease incidence, these susceptibles return (prematurely) to circulation (the blue hump). But, this offers fuel to the remaining embers of infection (at time 100), and a second wave ensues.</p>", "links"=>[], "tags"=>["idealized", "susceptible", "individuals", "self-isolate", "grows"], "article_id"=>584258, "categories"=>["Mathematics", "Biological Sciences", "Infectious Diseases"], "users"=>["Joshua M. Epstein", "Jon Parker", "Derek Cummings", "Ross A. Hammond"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003955.g003", "stats"=>{"downloads"=>1, "page_views"=>15, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_In_the_idealized_run_of_figure_3_susceptible_individuals_blue_curve_self_isolate_black_curve_through_fear_as_the_infection_of_disease_proper_grows_red_curve_/584258", "title"=>"In the idealized run of figure 3, susceptible individuals (blue-curve) self-isolate (black curve) through fear as the infection of disease proper grows (red curve).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:23:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/913582"], "description"=>"<p>(A&B): Classical SIR differential equations formulation and flowchart.</p>", "links"=>[], "tags"=>["differential", "equations", "formulation"], "article_id"=>584039, "categories"=>["Mathematics", "Biological Sciences", "Infectious Diseases"], "users"=>["Joshua M. Epstein", "Jon Parker", "Derek Cummings", "Ross A. Hammond"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003955.g001", "stats"=>{"downloads"=>3, "page_views"=>22, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_amp_B_Classical_SIR_differential_equations_formulation_and_flowchart_/584039", "title"=>"(A&B): Classical SIR differential equations formulation and flowchart.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:22:23"}
  • {"files"=>["https://ndownloader.figshare.com/files/914158"], "description"=>"<p>The percentage of runs (out of 30) for each parameter setting in which the epidemic spreads fully across the landscape, from an index case in one corner of the lattice all the way to the opposite corner.</p>", "links"=>[], "tags"=>["runs", "parameter", "spreads", "lattice"], "article_id"=>584620, "categories"=>["Mathematics", "Biological Sciences", "Infectious Diseases"], "users"=>["Joshua M. Epstein", "Jon Parker", "Derek Cummings", "Ross A. Hammond"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003955.g007", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_percentage_of_runs_out_of_30_for_each_parameter_setting_in_which_the_epidemic_spreads_fully_across_the_landscape_from_an_index_case_in_one_corner_of_the_lattice_all_the_way_to_the_opposite_corner_/584620", "title"=>"The percentage of runs (out of 30) for each parameter setting in which the epidemic spreads fully across the landscape, from an index case in one corner of the lattice all the way to the opposite corner.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:25:40"}
  • {"files"=>["https://ndownloader.figshare.com/files/914318"], "description"=>"<p>Each agent is represented by a colored dot on the lattice.</p>", "links"=>[], "tags"=>["screenshots", "agent-based", "simulation"], "article_id"=>584778, "categories"=>["Mathematics", "Biological Sciences", "Infectious Diseases"], "users"=>["Joshua M. Epstein", "Jon Parker", "Derek Cummings", "Ross A. Hammond"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003955.g009", "stats"=>{"downloads"=>5, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_amp_B_Screenshots_from_the_agent_based_simulation_model_without_and_with_flight_/584778", "title"=>"(A&B): Screenshots from the agent-based simulation model without and with flight.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:26:42"}
  • {"files"=>["https://ndownloader.figshare.com/files/913678"], "description"=>"<p>One would expect that if we set <i>α</i> = <i>β</i>, the disease and fear epidemic S-curves should coincide, but this is not the case. Fear (the green curve) precedes disease (the red curve).</p>", "links"=>[], "tags"=>["coupled"], "article_id"=>584140, "categories"=>["Mathematics", "Biological Sciences", "Infectious Diseases"], "users"=>["Joshua M. Epstein", "Jon Parker", "Derek Cummings", "Ross A. Hammond"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003955.g002", "stats"=>{"downloads"=>1, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Here_we_provide_the_coupled_case_with_945_8202_8202_946_8202_8202_0_0008_/584140", "title"=>"Here we provide the coupled case with α = β = 0.0008.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:23:00"}
  • {"files"=>["https://ndownloader.figshare.com/files/913908"], "description"=>"<p>All agents are “ignorers.” Parameterized in this way, the model produces quintessential SIR curves.</p>", "links"=>[], "tags"=>["adapts"], "article_id"=>584368, "categories"=>["Mathematics", "Biological Sciences", "Infectious Diseases"], "users"=>["Joshua M. Epstein", "Jon Parker", "Derek Cummings", "Ross A. Hammond"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003955.g004", "stats"=>{"downloads"=>2, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_We_consider_a_simple_form_of_the_model_in_which_fear_propagates_but_no_one_adapts_their_behavior_in_response_/584368", "title"=>"We consider a simple form of the model in which fear propagates, but no one adapts their behavior in response.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:24:15"}
  • {"files"=>["https://ndownloader.figshare.com/files/913978"], "description"=>"<p>Each bar in the chart represents an average across 30 simulation runs for a given parameter setting, with standard error range. When all agents hide, the epidemic is shorter and has substantially lower incidence that with no adaptive behavior. When a small percentage of agents flees (with the majority hiding), however, incidence goes up substantially even as the duration falls farther.</p>", "links"=>[], "tags"=>["duration", "incidence", "parameter"], "article_id"=>584433, "categories"=>["Mathematics", "Biological Sciences", "Infectious Diseases"], "users"=>["Joshua M. Epstein", "Jon Parker", "Derek Cummings", "Ross A. Hammond"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003955.g005", "stats"=>{"downloads"=>4, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_amp_B_Epidemic_duration_and_total_incidence_under_three_different_parameter_settings_/584433", "title"=>"(A&B): Epidemic duration and total incidence under three different parameter settings.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:24:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/914399"], "description"=>"<p>Summary of flight results.</p>", "links"=>[], "tags"=>["Computational biology", "Infectious diseases", "mathematics/nonlinear dynamics"], "article_id"=>584854, "categories"=>["Mathematics", "Biological Sciences", "Infectious Diseases"], "users"=>["Joshua M. Epstein", "Jon Parker", "Derek Cummings", "Ross A. Hammond"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003955.t002", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Summary_of_flight_results_/584854", "title"=>"Summary of flight results.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 07:27:07"}
  • {"files"=>["https://ndownloader.figshare.com/files/914245"], "description"=>"<p>Without flight the epidemic takes roughly 600 time periods to cross the lattice.</p>", "links"=>[], "tags"=>["cases", "spreads", "lattice", "takes", "longer"], "article_id"=>584697, "categories"=>["Mathematics", "Biological Sciences", "Infectious Diseases"], "users"=>["Joshua M. Epstein", "Jon Parker", "Derek Cummings", "Ross A. Hammond"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003955.g008", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_In_rare_cases_where_the_epidemic_spreads_fully_across_the_lattice_without_flight_it_takes_much_longer_to_do_so_than_in_cases_with_flight_/584697", "title"=>"In rare cases where the epidemic spreads fully across the lattice without flight, it takes much longer to do so than in cases with flight.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:26:13"}
  • {"files"=>["https://ndownloader.figshare.com/files/914081"], "description"=>"<p>As before, each bar in the chart represents an average across 30 simulation runs for a given parameter setting, with standard error range. The runs with 10% “ignorers” have similar incidence to runs with 100% “hiders,” and similar duration to runs with 100% “ignorers.” By contrast, the runs with 10% “fleers” have much higher incidence and lower duration.</p>", "links"=>[], "tags"=>["duration", "incidence"], "article_id"=>584540, "categories"=>["Mathematics", "Biological Sciences", "Infectious Diseases"], "users"=>["Joshua M. Epstein", "Jon Parker", "Derek Cummings", "Ross A. Hammond"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0003955.g006", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_amp_B_A_comparison_of_epidemic_duration_and_total_incidence_with_10_8220_fleers_8221_versus_10_8220_ignorers_8221_/584540", "title"=>"(A&B): A comparison of epidemic duration and total incidence with 10% “fleers” versus 10% “ignorers.”", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:25:14"}

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Relative Metric

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