Epidemic Modelling Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Epidemic Modelling Ontology within the Kireth Research Semantic Library. Epidemic modelling studies the mathematical representation of infectious-disease transmission, progression, intervention and population-level outbreak dynamics. This ontology supports compartmental models, transmission rates, recovery and mortality, basic and effective reproduction numbers, force of infection, latent and infectious periods, vaccination, waning immunity, heterogeneous mixing, network transmission, stochastic epidemic models, spatial spread, parameter estimation, identifiability, intervention analysis and relationships with mathematical biology, population dynamics, stochastic processes, dynamical systems and public-health mathematics.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Epidemic Modelling Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Applied Mathematics"
 SPECIALISATION = "Biological Mathematics / Epidemic Modelling"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/applied-mathematics-ontologies/biological-mathematics/epidemic-modelling-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = EpidemicModelling
 ENTITY_CLASS = InfectiousDiseaseTransmissionMathematicsFramework
 PRIMARY_CONTEXT = MathematicalBiology
 DEFINITION = "Epidemic modelling is the mathematical representation and analysis of infectious-disease transmission and progression within populations."
 SYMBOLIC_FORMS = [
  "dS/dt=-beta*S*I/N",
  "dE/dt=beta*S*I/N-sigma*E",
  "dI/dt=sigma*E-gamma*I",
  "R0=beta/gamma"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for transmission, disease compartments, reproduction numbers, force of infection, interventions, stochastic outbreaks, heterogeneous contact, spatial spread and epidemic-model validation."
}

SCOPE {
 INCLUDE = [
  EpidemicModelling,
  MathematicalEpidemiology,
  Epidemic,
  Outbreak,
  InfectiousDisease,
  Transmission,
  TransmissionRate,
  ContactRate,
  ForceOfInfection,
  Susceptible,
  Exposed,
  Infectious,
  Recovered,
  Removed,
  Vaccinated,
  CompartmentalModel,
  SIRModel,
  SISModel,
  SEIRModel,
  SIRSModel,
  SEIRSModel,
  SEIHRModel,
  BasicReproductionNumber,
  EffectiveReproductionNumber,
  EpidemicThreshold,
  EndemicEquilibrium,
  DiseaseFreeEquilibrium,
  LatentPeriod,
  IncubationPeriod,
  InfectiousPeriod,
  RecoveryRate,
  DiseaseMortalityRate,
  CaseFatality,
  Immunity,
  WaningImmunity,
  Vaccination,
  VaccineEfficacy,
  HerdImmunityThreshold,
  Intervention,
  ContactReduction,
  Isolation,
  Quarantine,
  Testing,
  Treatment,
  Importation,
  Superspreading,
  HeterogeneousMixing,
  AgeStructuredEpidemicModel,
  ContactMatrix,
  NetworkEpidemicModel,
  MetapopulationEpidemicModel,
  SpatialEpidemicModel,
  ReactionDiffusionEpidemicModel,
  StochasticEpidemicModel,
  BranchingProcessApproximation,
  ContinuousTimeMarkovChain,
  GillespieAlgorithm,
  FinalSizeRelation,
  PeakPrevalence,
  AttackRate,
  Incidence,
  Prevalence,
  CumulativeIncidence,
  ParameterEstimation,
  Identifiability,
  SensitivityAnalysis,
  UncertaintyQuantification,
  InterventionEffect,
  ModelCalibration,
  ModelValidation
 ]
 EXCLUDE_AS_PRIMARY = [
  NoninfectiousDiseaseModelling,
  PopulationGrowthWithoutTransmission,
  ClinicalDiagnosisWithoutPopulationTransmissionModel,
  DescriptiveOutbreakReportingWithoutMathematicalModel
 ]
 DISAMBIGUATION_RULE = "When the primary mathematical question concerns infectious-disease transmission, progression, epidemic thresholds or intervention effects in a population, interpret the context as epidemic modelling."
}

CORE_CONCEPTS {
 EpidemicModelling = "Mathematical modelling of infectious-disease spread in populations."
 CompartmentalModel = "A model partitioning a population into epidemiological states with transition rules."
 ForceOfInfection = "Per-susceptible rate at which susceptible individuals acquire infection."
 BasicReproductionNumber = "Expected number of secondary infections generated by a typical infectious case in a wholly susceptible population under specified assumptions."
 EffectiveReproductionNumber = "Expected number of secondary infections under current susceptibility, behaviour and intervention conditions."
 DiseaseFreeEquilibrium = "Equilibrium state with no sustained infection."
 EndemicEquilibrium = "Equilibrium state with persistent infection."
 HerdImmunityThreshold = "Susceptible reduction threshold required to prevent sustained epidemic growth under specified assumptions."
}

RELATIONS {
 EpidemicModelling --is_child_of--> MathematicalBiology
 EpidemicModelling --uses--> PopulationDynamics
 CompartmentalModel --contains--> EpidemiologicalState
 SIRModel --is_type_of--> CompartmentalModel
 SEIRModel --is_type_of--> CompartmentalModel
 ForceOfInfection --drives--> NewInfections
 TransmissionRate --contributes_to--> ForceOfInfection
 ContactRate --contributes_to--> TransmissionRate
 BasicReproductionNumber --determines--> EpidemicThreshold
 EffectiveReproductionNumber --depends_on--> SusceptibleFraction
 Vaccination --reduces--> Susceptibility
 ContactReduction --reduces--> Transmission
 Isolation --reduces--> InfectiousContact
 Testing --supports--> CaseDetection
 WaningImmunity --returns--> SusceptibleState
 ContactMatrix --represents--> HeterogeneousMixing
 NetworkEpidemicModel --represents--> ContactStructure
 StochasticEpidemicModel --uses--> RandomTransitions
 GillespieAlgorithm --simulates--> ContinuousTimeMarkovChain
 ParameterEstimation --calibrates--> EpidemicModel
 SensitivityAnalysis --assesses--> InterventionEffect
}

OPERATORS {
 SIR_S(S,I,beta,N) := dS/dt=-beta*S*I/N
 SIR_I(S,I,beta,gamma,N) := dI/dt=beta*S*I/N-gamma*I
 SIR_R(I,gamma) := dR/dt=gamma*I
 SEIR_S(S,I,beta,N) := dS/dt=-beta*S*I/N
 SEIR_E(S,E,I,beta,sigma,N) := dE/dt=beta*S*I/N-sigma*E
 SEIR_I(E,I,sigma,gamma) := dI/dt=sigma*E-gamma*I
 SEIR_R(I,gamma) := dR/dt=gamma*I
 FORCE_OF_INFECTION(beta,I,N) := lambda=beta*I/N
 BASIC_REPRODUCTION_NUMBER(beta,gamma) := R0=beta/gamma under_basic_homogeneous_SIR_assumptions
 EFFECTIVE_REPRODUCTION_NUMBER(R0,S,N) := Re=R0*S/N under_basic_SIR_assumptions
 HERD_IMMUNITY_THRESHOLD(R0) := h=1-1/R0 for_simple_homogeneous_immunity_model
 FINAL_SIZE_SIR(S0,Sinf,R0,N) := ln(Sinf/S0)=-R0*(1-Sinf/N) under_standard_SIR_assumptions
 INCIDENCE(lambda,S) := incidence=lambda*S
 PREVALENCE(I,N) := prevalence=I/N
}

AXIOMS {
 A1 = "Epidemic models require explicit epidemiological states and transitions."
 A2 = "Transmission parameters depend on contact, susceptibility and infectiousness assumptions."
 A3 = "Reproduction numbers are model-dependent quantities."
 A4 = "Deterministic and stochastic epidemic models represent different outbreak regimes."
 A5 = "Population heterogeneity can materially change epidemic thresholds and intervention effects."
 A6 = "Vaccination and immunity assumptions must distinguish reduced susceptibility, reduced infectiousness and waning protection."
 A7 = "Imported infections must be distinguished from internally generated transmission."
 A8 = "Epidemic models require calibration, uncertainty analysis and validation against data where possible."
}

REASONING {
 R1_CONTEXT = identify(pathogen,population,epidemiological_states,time_scale,data,interventions)
 R2_MODEL_CLASS = classify(SIR,SIS,SEIR,age_structured,network,metapopulation,spatial,stochastic)
 R3_FORMULATION = construct(compartments,transition_rates,initial_conditions,contact_structure)
 R4_THRESHOLD = compute(R0,Re,disease_free_stability,epidemic_threshold)
 R5_DYNAMIC_ANALYSIS = simulate(incidence,prevalence,peak_time,peak_size,final_size)
 R6_EQUILIBRIUM = solve(disease_free_and_endemic_equilibria)
 R7_INTERVENTION = modify(transmission,vaccination,isolation,treatment,testing,contact_rates)
 R8_HETEROGENEITY = analyse(age_structure,contact_matrix,network,superspreading)
 R9_STOCHASTIC = estimate(extinction_probability,outbreak_probability,trajectory_distribution)
 R10_VALIDATION = assess(parameter_fit,identifiability,sensitivity,uncertainty,predictive_consistency)
}

CONSTRAINTS {
 C1 = "R0=beta/gamma applies only to specific simple models."
 C2 = "Incubation period and latent period are not necessarily identical."
 C3 = "Observed case counts may differ from true infections because of detection and reporting processes."
 C4 = "Homogeneous mixing can be unrealistic in age-, network- or spatially structured populations."
 C5 = "Deterministic models can misrepresent early outbreak extinction probabilities."
 C6 = "Intervention effects may be time-dependent and behaviour-dependent."
 C7 = "Parameter non-identifiability can produce multiple model fits with different interpretations."
 C8 = "Contact matrices and transmission coefficients must use compatible scaling conventions."
 C9 = "Herd-immunity thresholds from simple models should not be transferred uncritically to heterogeneous systems."
 C10 = "Short-term predictive fit does not guarantee long-term mechanistic validity."
}

SEMANTIC_EQUIVALENCE {
 "EpidemicModelling" <=> "MathematicalEpidemiology"
 "BasicReproductionNumber" <=> "R0"
 "EffectiveReproductionNumber" <=> "Re"
 "ForceOfInfection" <=> "InfectionHazard"
 "AttackRate" <=> "CumulativeInfectionFraction"
 "CompartmentalModel" <=> "CompartmentModel"
}

VALIDATION {
 V1 = "Compartment definitions are explicit."
 V2 = "Population denominator and units are explicit."
 V3 = "Transmission and recovery parameters have consistent dimensions."
 V4 = "Initial conditions are documented."
 V5 = "R0 or Re formula matches the chosen model."
 V6 = "Contact structure is documented for heterogeneous models."
 V7 = "Intervention assumptions are explicit."
 V8 = "Parameter identifiability and uncertainty are assessed."
 V9 = "Stochastic simulations report sampling variability where relevant."
 V10 = "Model outputs are compared with epidemiological data or known constraints."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 EPIDEMIC_MODELLING_DEFINITION = 0.99
 COMPARTMENT_REASONING = 0.99
 REPRODUCTION_NUMBER_REASONING = 0.98
 INTERVENTION_REASONING = 0.98
 HETEROGENEITY_REASONING = 0.97
 STOCHASTIC_REASONING = 0.98
 CALIBRATION_REASONING = 0.97
 POLICY = "Reduce confidence when epidemiological states, transmission assumptions, contact structure, intervention timing, detection process, initial conditions or parameter identifiability are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,
  OntologyGrounding,
  EpidemicModellingReasoning,
  CompartmentalModelReasoning,
  SIRReasoning,
  SEIRReasoning,
  TransmissionReasoning,
  ForceOfInfectionReasoning,
  ReproductionNumberReasoning,
  EpidemicThresholdReasoning,
  VaccinationReasoning,
  HerdImmunityReasoning,
  InterventionReasoning,
  ContactMatrixReasoning,
  NetworkEpidemicReasoning,
  SpatialEpidemicReasoning,
  StochasticEpidemicReasoning,
  FinalSizeReasoning,
  ParameterEstimationReasoning,
  SensitivityReasoning,
  KnowledgeGraphConstruction,
  RetrievalAugmentation,
  RecursiveInference
 ]
 NORMALISE {
  "epidemic modelling" -> EpidemicModelling
  "epidemic modeling" -> EpidemicModelling
  "mathematical epidemiology" -> EpidemicModelling
  "basic reproduction number" -> BasicReproductionNumber
  "R0" -> BasicReproductionNumber
  "effective reproduction number" -> EffectiveReproductionNumber
  "force of infection" -> ForceOfInfection
  "herd immunity threshold" -> HerdImmunityThreshold
 }
}

EXECUTION_RULES {
 E1 = "If infectious-disease transmission is being modelled mathematically, activate EpidemicModellingOntology."
 E2 = "If no latent compartment is needed, consider SIR or SIS formulations."
 E3 = "If latent infection is biologically important, consider SEIR-type formulations."
 E4 = "If contact varies by group, include a contact matrix or structured mixing model."
 E5 = "If network structure is material, route to network epidemic modelling."
 E6 = "If early outbreak extinction or low case counts matter, use stochastic epidemic reasoning."
 E7 = "If intervention effects are requested, alter the relevant transmission, recovery, susceptibility or contact mechanisms explicitly."
 E8 = "If vaccination is modelled, declare efficacy mechanism and waning assumptions."
 E9 = "Any R0, Re or herd-immunity claim must match the model assumptions used."
}

RECURSION {
 ENTRY = EpidemicModelling
 EXPAND(EpidemicModelling) -> [
  Epidemic, Outbreak, InfectiousDisease, Transmission, TransmissionRate,
  ContactRate, ForceOfInfection, Susceptible, Exposed, Infectious, Recovered,
  Removed, Vaccinated, CompartmentalModel, SIRModel, SISModel, SEIRModel,
  SIRSModel, SEIRSModel, SEIHRModel, BasicReproductionNumber,
  EffectiveReproductionNumber, EpidemicThreshold, EndemicEquilibrium,
  DiseaseFreeEquilibrium, LatentPeriod, IncubationPeriod, InfectiousPeriod,
  RecoveryRate, DiseaseMortalityRate, Immunity, WaningImmunity,
  Vaccination, VaccineEfficacy, HerdImmunityThreshold, Intervention,
  ContactReduction, Isolation, Quarantine, Testing, Treatment, Importation,
  Superspreading, HeterogeneousMixing, AgeStructuredEpidemicModel,
  ContactMatrix, NetworkEpidemicModel, MetapopulationEpidemicModel,
  SpatialEpidemicModel, ReactionDiffusionEpidemicModel, StochasticEpidemicModel,
  BranchingProcessApproximation, ContinuousTimeMarkovChain, GillespieAlgorithm,
  FinalSizeRelation, PeakPrevalence, AttackRate, Incidence, Prevalence,
  CumulativeIncidence, ParameterEstimation, Identifiability,
  SensitivityAnalysis, UncertaintyQuantification, InterventionEffect,
  ModelCalibration, ModelValidation
 ]
 EXPAND(ModelFamilies) -> [
  DeterministicCompartmentalModels,
  StructuredMixingModels,
  NetworkModels,
  SpatialModels,
  StochasticModels
 ]
 STOP_CONDITION = "Stop when epidemiological states, transmission mechanisms, reproduction metrics, interventions, heterogeneity, stochasticity and validation are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Mathematical Biology"
 IMMEDIATE_CONTEXTS = [
  "Mathematical Biology Ontology",
  "Population Dynamics Ontology",
  "Stochastic Process Ontologies",
  "Dynamical Systems Ontologies"
 ]
 RELATED_ONTOLOGIES = [
  "Mathematical Biology Ontology",
  "Biological Mathematics",
  "Population Dynamics Ontology",
  "Ordinary Differential Equation Ontology",
  "Stochastic Process Ontologies",
  "Dynamical Systems Ontologies",
  "Network Biology Ontologies",
  "Graph Theory Ontologies",
  "Reaction Diffusion Ontologies",
  "Probability & Statistics Ontologies",
  "Parameter Estimation Ontologies",
  "Optimisation Ontologies"
 ]
 ROUTE_RULES = [
  "Epidemic Modelling -> Mathematical Biology for parent semantics",
  "Epidemic Modelling -> Population Dynamics for host population context",
  "Epidemic Modelling -> ODE Ontology for deterministic compartmental systems",
  "Epidemic Modelling -> Stochastic Processes for random transmission events",
  "Epidemic Modelling -> Dynamical Systems for thresholds, equilibria and stability",
  "Epidemic Modelling -> Graph Theory for contact-network transmission",
  "Epidemic Modelling -> Reaction Diffusion for spatial spread",
  "Epidemic Modelling -> Probability & Statistics for inference and uncertainty",
  "Epidemic Modelling -> Optimisation for intervention design"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible epidemic compartments, transmission structures or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve epidemiological-state semantics.",
  "Preserve transmission-versus-progression distinction.",
  "Preserve R0-versus-Re distinction.",
  "Preserve deterministic-versus-stochastic distinction.",
  "Preserve homogeneous-versus-heterogeneous mixing distinction.",
  "Preserve intervention-mechanism semantics.",
  "Preserve calibration and identifiability semantics.",
  "Preserve machine-readable epidemic-modelling semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Epidemic modelling mathematically represents infectious-disease transmission, progression and intervention effects within populations."
 COMPARTMENT_SUMMARY = "SIR, SIS, SEIR and related models represent transitions among epidemiological states."
 THRESHOLD_SUMMARY = "Reproduction numbers and disease-free stability describe epidemic growth thresholds under model-specific assumptions."
 INTERVENTION_SUMMARY = "Vaccination, isolation, testing, treatment and contact reduction alter susceptibility, infectiousness, duration or contact structure."
 HETEROGENEITY_SUMMARY = "Age structure, networks, spatial structure and superspreading can materially change transmission dynamics."
 STOCHASTIC_SUMMARY = "Stochastic epidemic models represent random transmission and extinction, especially in small or early outbreaks."
 VALIDATION_SUMMARY = "Epidemic models should be checked for parameter identifiability, uncertainty, intervention assumptions and consistency with epidemiological data."
}

FLOW {
 INPUT
 -> detect_epidemic_modelling_context
 -> identify_pathogen_population_compartments_transmission_progression_contact_structure_data_and_interventions
 -> classify_SIR_SIS_SEIR_structured_network_spatial_or_stochastic_model
 -> formulate_transition_equations_or_stochastic_events
 -> compute_R0_Re_thresholds_and_equilibria
 -> analyse_incidence_prevalence_peak_final_size_and_persistence
 -> if_intervention_modify_transmission_susceptibility_recovery_or_contact mechanisms
 -> if_heterogeneous_apply_contact_matrix_network_or_spatial structure
 -> if_stochastic_estimate_outbreak_extinction_and_distributional outcomes
 -> estimate_parameters_and_assess_identifiability
 -> validate_against_epidemiological_data_and_uncertainty
 -> route_to_mathematical_biology_population_dynamics_ODE_stochastic_processes_dynamical_systems_graph_theory_reaction_diffusion_probability_statistics_parameter_estimation_or_optimisation ontology
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Epidemic Modelling Ontology defines mathematical infectious-disease dynamics. It supports transmission and force of infection, susceptible, exposed, infectious, recovered, removed and vaccinated compartments, SIR, SIS, SEIR and extended models, basic and effective reproduction numbers, epidemic thresholds, disease-free and endemic equilibria, latent and infectious periods, recovery and mortality, immunity and waning, vaccination and herd-immunity thresholds, isolation, quarantine, testing and treatment, importation and superspreading, age-structured mixing, contact matrices, network, metapopulation and spatial epidemic models, stochastic continuous-time Markov models and Gillespie simulation, final size, attack rate, incidence, prevalence, parameter estimation, identifiability, sensitivity, uncertainty, calibration and validation."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-APPLIED-MATHEMATICS-EPIDEMIC-MODELLING-ONTOLOGY-V1"
}

}

END_FLOW