{"id":"W2607311294","doi":"10.1007/978-3-319-56433-3_11","title":"The Theory of Basic Reproduction Ratios","year":2017,"lang":"en","type":"book-chapter","venue":"CMS books in mathematics","topic":"Mathematical and Theoretical Epidemiology and Ecology Models","field":"Medicine","cited_by":11,"is_retracted":false,"has_abstract":false,"ca_institutions":"Memorial University of Newfoundland","funders":"","keywords":"Ode; Basic reproduction number; Population; Mathematics; Spectral radius; Ordinary differential equation; Applied mathematics; Infectious disease (medical specialty); Stability (learning theory); Mathematical modelling of infectious disease; Pure mathematics; Calculus (dental); Eigenvalues and eigenvectors; Differential equation; Mathematical analysis; Demography; Computer science; Physics; Disease; Medicine","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001146665,0.000965214,0.001060411,0.001456255,0.0006774821,0.003427716,0.001610367,0.001820576,0.01586252],"category_scores_gemma":[0.003673127,0.0005993762,0.0008025109,0.001767246,0.004644934,0.00466213,0.001110357,0.004427413,0.00671825],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001922752,"about_ca_system_score_gemma":0.001070863,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009186363,"about_ca_topic_score_gemma":0.0006528296,"domain_scores_codex":[0.9993653,0.0002222782,0.00003144243,0.0001156942,0.0002177633,0.00004754924],"domain_scores_gemma":[0.998872,0.0007396578,0.00006699204,0.0001324265,0.0001430485,0.00004588187],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000002583579,0.000004423878,0.00003130745,0.00004504744,0.000004046757,0.00001416282,0.00005042987,0.0004649964,0.0001041957,0.9807034,0.008210383,0.01036511],"study_design_scores_gemma":[0.00000277351,0.000004014804,0.00008354282,0.00002962541,0.000002413581,0.0000642243,0.00001495318,0.0006895841,0.00004616049,0.9549731,0.04408463,0.000005088874],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"methods","genre_scores_codex":[0.004038685,0.07304928,0.1833809,0.009308871,0.002883542,0.00004652638,0.0006472995,0.0003713312,0.7262736],"genre_scores_gemma":[0.3079414,0.1010034,0.1313359,0.00751661,0.01206206,0.000589321,0.001138515,0.0005764129,0.4378363],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.01586252,"threshold_uncertainty_score":0.05306542,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05931377983814449,"score_gpt":0.30237389995081,"score_spread":0.2430601201126656,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}