Bayesian History Matching of Complex Infectious Disease Models Using Emulation: A Tutorial and a Case Study on HIV in Uganda
Publication Date
January 08, 2015
Journal
PLOS Computational Biology
Authors
Ioannis Andrianakis, Ian R. Vernon, Nicky Mc Creesh, Trevelyan J. Mc Kinley, et al
Volume
11
Issue
1
Pages
e1003968
DOI
http://doi.org/10.1371/journal.pcbi.1003968
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1003968
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/25569850
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4288726
Europe PMC
http://europepmc.org/abstract/MED/25569850
Web of Science
000349309400005
Scopus
84922219924
Mendeley
http://www.mendeley.com/research/bayesian-history-matching-complex-infectious-disease-models-using-emulation-tutorial-case-study-hiv
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Mendeley | Further Information

{"title"=>"Bayesian History Matching of Complex Infectious Disease Models Using Emulation: A Tutorial and a Case Study on HIV in Uganda", "type"=>"journal", "authors"=>[{"first_name"=>"Ioannis", "last_name"=>"Andrianakis", "scopus_author_id"=>"57194113361"}, {"first_name"=>"Ian R.", "last_name"=>"Vernon", "scopus_author_id"=>"8548510600"}, {"first_name"=>"Nicky", "last_name"=>"McCreesh", "scopus_author_id"=>"54393598300"}, {"first_name"=>"Trevelyan J.", "last_name"=>"McKinley", "scopus_author_id"=>"24174960600"}, {"first_name"=>"Jeremy E.", "last_name"=>"Oakley", "scopus_author_id"=>"7005900038"}, {"first_name"=>"Rebecca N.", "last_name"=>"Nsubuga", "scopus_author_id"=>"36806561500"}, {"first_name"=>"Michael", "last_name"=>"Goldstein", "scopus_author_id"=>"7403013913"}, {"first_name"=>"Richard G.", "last_name"=>"White", "scopus_author_id"=>"8781712900"}], "year"=>2015, "source"=>"PLoS Computational Biology", "identifiers"=>{"scopus"=>"2-s2.0-84922219924", "issn"=>"15537358", "pmid"=>"25569850", "isbn"=>"1553-7358 (Electronic)\\r1553-734X (Linking)", "doi"=>"10.1371/journal.pcbi.1003968", "pui"=>"602059671", "sgr"=>"84922219924"}, "id"=>"15a77780-ed80-3bc5-8bfe-92c012bf08f6", "abstract"=>"Advances in scientific computing have allowed the development of complex models that are being routinely applied to problems in disease epidemiology, public health and decision making. The utility of these models depends in part on how well they can reproduce empirical data. However, fitting such models to real world data is greatly hindered both by large numbers of input and output parameters, and by long run times, such that many modelling studies lack a formal calibration methodology. We present a novel method that has the potential to improve the calibration of complex infectious disease models (hereafter called simulators). We present this in the form of a tutorial and a case study where we history match a dynamic, event-driven, individual-based stochastic HIV simulator, using extensive demographic, behavioural and epidemiological data available from Uganda. The tutorial describes history matching and emulation. History matching is an iterative procedure that reduces the simulator's input space by identifying and discarding areas that are unlikely to provide a good match to the empirical data. History matching relies on the computational efficiency of a Bayesian representation of the simulator, known as an emulator. Emulators mimic the simulator's behaviour, but are often several orders of magnitude faster to evaluate. In the case study, we use a 22 input simulator, fitting its 18 outputs simultaneously. After 9 iterations of history matching, a non-implausible region of the simulator input space was identified that was 10(11) times smaller than the original input space. Simulator evaluations made within this region were found to have a 65% probability of fitting all 18 outputs. History matching and emulation are useful additions to the toolbox of infectious disease modellers. 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CrossRef

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1862549"], "description"=>"<p>Minimum implausibility plots show an estimate of the minimum implausibility for different values of pairs of inputs. Optical depth plots show an estimate of the probability of encountering a non-implausible point for different values of pairs of inputs.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286144, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.g005", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Minimum_implausibility_a_and_optical_depth_b_plots_for_inputs_1_and_4_in_wave_1_/1286144", "title"=>"Minimum implausibility (a) and optical depth (b) plots for inputs 1 and 4 in wave 1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862616"], "description"=>"<p>The black lines show the average observed HIV prevalence with 95% credible ranges.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286177, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.g008", "stats"=>{"downloads"=>0, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulator_output_male_and_female_HIV_prevalence_in_waves_1_4_7_and_10_/1286177", "title"=>"Simulator output (male and female HIV prevalence) in waves 1, 4, 7 and 10.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862619"], "description"=>"<p>Each of the 18 panels shows the range of the target data (horizontal region) and the simulator's output in waves 1 (red), 4 (yellow), 7 (blue) and 10 (green) (left to right along the x-axis).</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286180, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.g009", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Convergence_of_the_simulator_s_output_to_the_empirical_data_with_successive_waves_of_history_matching_/1286180", "title"=>"Convergence of the simulator's output to the empirical data with successive waves of history matching.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862629"], "description"=>"<p>Each panel shows the samples drawn for one of the 22 simulator inputs. Their full names and descriptions can be found in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003968#pcbi-1003968-t001\" target=\"_blank\">Table 1</a>.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286182, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.g010", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Posterior_samples_drawn_with_the_importance_sampling_method_described_in_section_8216_Posterior_Sampling_8217_/1286182", "title"=>"Posterior samples drawn with the importance sampling method described in section ‘Posterior Sampling’.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862630"], "description"=>"<p>These define the input parameter space over which the history match search is performed.</p><p>*The simulator input parameters that codetermine partnership formation. The actual rate of partnership formation in the simulator will vary from this due to adjustment for concurrency and partnership balancing.</p><p>Simulator input parameter description and ranges.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286183, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.t001", "stats"=>{"downloads"=>0, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Simulator_input_parameter_description_and_ranges_/1286183", "title"=>"Simulator input parameter description and ranges.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862631"], "description"=>"<p>Description of simulator outputs and limits defined as an acceptable match.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286184, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.t002", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Description_of_simulator_outputs_and_limits_defined_as_an_acceptable_match_/1286184", "title"=>"Description of simulator outputs and limits defined as an acceptable match.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862632"], "description"=>"<p>At wave 9, the non-implausible region is a tiny fraction (10<sup>−11</sup>) of the original input space, implying that we have learnt a large amount from the history matching process.</p><p>Acceptance rates for the 9 waves, expressing the probability that an input drawn at random from the original input space passes the wave's implausibility test.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286185, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.t003", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Acceptance_rates_for_the_9_waves_expressing_the_probability_that_an_input_drawn_at_random_from_the_original_input_space_passes_the_wave_s_implausibility_test_/1286185", "title"=>"Acceptance rates for the 9 waves, expressing the probability that an input drawn at random from the original input space passes the wave's implausibility test.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862633"], "description"=>"<p>Percentage of the non-implausible space at wave 9 that would be calculated as implausible if the uncertainty shown in the first row was reduced by the amount shown in the first column.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286186, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.t004", "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Percentage_of_the_non_implausible_space_at_wave_9_that_would_be_calculated_as_implausible_if_the_uncertainty_shown_in_the_first_row_was_reduced_by_the_amount_shown_in_the_first_column_/1286186", "title"=>"Percentage of the non-implausible space at wave 9 that would be calculated as implausible if the uncertainty shown in the first row was reduced by the amount shown in the first column.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862634", "https://ndownloader.figshare.com/files/1862635", "https://ndownloader.figshare.com/files/1862636"], "description"=>"<div><p>Advances in scientific computing have allowed the development of complex models that are being routinely applied to problems in disease epidemiology, public health and decision making. The utility of these models depends in part on how well they can reproduce empirical data. However, fitting such models to real world data is greatly hindered both by large numbers of input and output parameters, and by long run times, such that many modelling studies lack a formal calibration methodology. We present a novel method that has the potential to improve the calibration of complex infectious disease models (hereafter called <i>simulators</i>). We present this in the form of a tutorial and a case study where we history match a dynamic, event-driven, individual-based stochastic HIV simulator, using extensive demographic, behavioural and epidemiological data available from Uganda. The tutorial describes history matching and emulation. History matching is an iterative procedure that reduces the simulator's input space by identifying and discarding areas that are unlikely to provide a good match to the empirical data. History matching relies on the computational efficiency of a Bayesian representation of the simulator, known as an <i>emulator</i>. Emulators mimic the simulator's behaviour, but are often several orders of magnitude faster to evaluate. In the case study, we use a 22 input simulator, fitting its 18 outputs simultaneously. After 9 iterations of history matching, a non-implausible region of the simulator input space was identified that was times smaller than the original input space. Simulator evaluations made within this region were found to have a 65% probability of fitting all 18 outputs. History matching and emulation are useful additions to the toolbox of infectious disease modellers. Further research is required to explicitly address the stochastic nature of the simulator as well as to account for correlations between outputs.</p></div>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286187, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003968.s001", "https://dx.doi.org/10.1371/journal.pcbi.1003968.s002", "https://dx.doi.org/10.1371/journal.pcbi.1003968.s003"], "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Bayesian_History_Matching_of_Complex_Infectious_Disease_Models_Using_Emulation_A_Tutorial_and_a_Case_Study_on_HIV_in_Uganda_/1286187", "title"=>"Bayesian History Matching of Complex Infectious Disease Models Using Emulation: A Tutorial and a Case Study on HIV in Uganda", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862581"], "description"=>"<p>Minimum implausibility plots show an estimate of the minimum implausibility for different values of pairs of inputs. Optical depth plots show an estimate of the probability of encountering a non-implausible point for different values of pairs of inputs.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286159, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.g006", "stats"=>{"downloads"=>0, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Minimum_implausibility_below_and_left_of_diagonal_and_optical_depth_plots_above_and_right_of_diagonal_for_10_key_inputs_for_waves_1_4_7_9_/1286159", "title"=>"Minimum implausibility (below and left of diagonal) and optical depth plots (above and right of diagonal) for 10 key inputs for waves 1,4,7,9.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862593"], "description"=>"<p>Each line represents the percentage of each wave's simulator runs with an less than the value indicated by the x-axis.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286162, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.g007", "stats"=>{"downloads"=>0, "page_views"=>21, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Cumulative_distribution_function_of_simulator_run_implausibility_by_waves_/1286162", "title"=>"Cumulative distribution function of simulator run implausibility by waves.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862538"], "description"=>"<p>The physical process is observed via and described by the simulator output . The simulator is substituted by the emulator for computational efficiency. The question marks indicate the various sources of uncertainty present in the system.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286135, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.g001", "stats"=>{"downloads"=>0, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_History_matching_/1286135", "title"=>"History matching.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862539"], "description"=>"<p>The simulator is evaluated at carefully selected design points. Its output is used to train the emulator, which, with the help of the implausibility measure, determines the parts of the input space which are non-implausible (NI). The simulator is then evaluated at set of design points from the non-implausible space and the procedure is repeated until one or more stopping criteria are met.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286136, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.g002", "stats"=>{"downloads"=>0, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_History_matching_workflow_/1286136", "title"=>"History matching workflow.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862541"], "description"=>"<p>Panel (a) shows an emulator of the toy simulator (black dashed line). The value of is considered unknown apart from six points where the simulator is run and are represented by the black dots in the figure. The blue line is the emulator's posterior mean, and the red lines represent its posterior uncertainty (95% CI). The 3 horizontal lines represent the empirical data (mean value and 95% CI) that we use to history match the simulator. Panel (b) shows the implausibility for the emulator and the empirical data shown in panel (a). The implausibility is large when the emulator's posterior mean is far from the empirical data, relatively to the uncertainties present in the system (observation and code uncertainty in this case). The horizontal green line is an implausibility cut-off, which determines whether an input is implausible or not.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286138, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.g003", "stats"=>{"downloads"=>0, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Example_emulator_and_implausibility_for_toy_simulator_/1286138", "title"=>"Example emulator and implausibility for toy simulator [].", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-01-08 03:08:38"}
  • {"files"=>["https://ndownloader.figshare.com/files/1862542"], "description"=>"<p>Panel (a) shows an emulator of the toy simulator (black dashed line). The value of is considered unknown apart from seven points where the simulator is run and are represented by the black dots in the figure. The blue line is the emulator's posterior mean, and the red lines represent its posterior uncertainty (95% CI). The 3 horizontal lines represent the empirical data (mean value and 95% CI) that we use to history match the simulator. Panel (b) shows the implausibility for the emulator and the empirical data shown in panel (a). The implausibility is large when the emulator's posterior mean is far from the empirical data, relatively to the uncertainties present in the system (observation and code uncertainty in this case). The horizontal green line is an implausibility cut-off, which determines whether an input is implausible or not.</p>", "links"=>[], "tags"=>["18 outputs", "case study", "input space", "simulator input space", "modelling studies lack", "22 input simulator", "hiv", "data"], "article_id"=>1286139, "categories"=>["Uncategorised"], "users"=>["Ioannis Andrianakis", "Ian R. Vernon", "Nicky McCreesh", "Trevelyan J. McKinley", "Jeremy E. Oakley", "Rebecca N. Nsubuga", "Michael Goldstein", "Richard G. White"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1003968.g004", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Second_history_matching_wave_for_the_toy_simulator_/1286139", "title"=>"Second history matching wave for the toy simulator .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-01-08 03:08:38"}

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{"start_date"=>"2015-01-01T00:00:00Z", "end_date"=>"2015-12-31T00:00:00Z", "subject_areas"=>[]}
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