ODD Protocol for Infectious Disease Modeling

• ODD Protocol is a standardized framework for documenting agent-based models used in simulating infectious diseases, ensuring clarity and reproducibility.
• It details model design concepts such as agent behaviors, state transitions, and stochastic processes, which supports rigorous validation and cross-study comparisons.
• Its integration with compartmental SEIRS models and geospatial data enables accurate forecasting of epidemic trajectories and resource demands.

The ODD Protocol, in the context of infectious disease modeling, refers to the Overview, Design Concepts, and Details protocol. This protocol is employed for standardizing the documentation and communication of agent-based models (ABMs), particularly those used for simulating and forecasting infectious diseases. A prominent implementation is the ODD Protocol applied in the COVID-19 submodel for the NC MInD ABM, a geospatially explicit ABM framework developed under the North Carolina Modeling Infectious Diseases Program. The ODD Protocol enables rigorous specification of purpose, agent structures, state transitions, stochastic processes, and integration with compartmental models, thereby supporting reproducibility, model validation, and cross-study comparison (Jones et al., 2022).

1. Purpose, Scope, and Model Integration

The COVID-19 submodel utilizing the ODD Protocol is an extension of the NC MInD ABM, designed to simulate the trajectory of SARS-CoV-2 infections, within-host disease progression, and COVID-19–related hospitalizations at the individual (agent) level in the state of North Carolina. Its principal uses include:

• Forecasting hospital demand by projecting case-driven inpatient admissions.
• Estimating transmission and visitation patterns, with emphasis on high-risk settings such as nursing homes.
• Providing input parameters for within-hospital submodels (e.g., resource allocation, clinical workflow).

The submodel is not intended to generate scenario-based outcomes within the protocol description itself; these analyses are reserved for separate studies targeting use-case results (Jones et al., 2022).

2. Key Entities, State Variables, and Spatiotemporal Structure

The ODD Protocol mandates explicit delineation of:

• Entities:
  • Agents: Individuals in the model, each with age group, vaccination status, COVID-19 clinical state, and healthcare worker (HCW) designation.
  • Locations: Healthcare facilities (hospitals, nursing homes), each geolocated within county boundaries.
• Agent State Variables:
  • COVID-19 Status (integer): 1=Susceptible; 2=Asymptomatic; 3=Mild/Moderate; 4=Severe; 5=Critical; 6=Recovered.
  • Vaccination Status (Boolean): Static assignment at initialization.
  • HCW Flag (Boolean): Denotes assignment as healthcare worker.
• Spatiotemporal Scales:
  • Spatial: Home county attributes for agents, explicit NC county mapping for facilities.
  • Temporal: Discrete daily time steps with configurable horizon (default 30 days), lacking sub-daily structure.

3. Model Design Concepts and Algorithmic Implementation

The ODD Protocol organizes design under several core concepts:

• Theoretical Framework: The model couples agent-based dynamics with deterministic SEIRS compartmental models at the county level, driving forecasts of incident infections. Parameters (e.g., duration of infectiousness, case multipliers for underreporting) are expert-elicited and calibrated to observed epidemiological data.
• Agent Behavior:
  • No adaptation or learning; both vaccination and HCW assignments are fixed at initialization.
  • Behavioral changes are driven by current health status: symptomatic agents reduce work attendance by 20 percentage points and nursing home visitation by 60 percentage points; asymptomatic agents show no change.
• Contact Structures:
  • Nursing home residents may receive up to three community visitors daily, drawn by age and visitation probability.
  • HCWs interact with facilities as single-site, multisite, part-time, or contract employees. Disease transmission between agents is not simulated directly; all new infections are imposed according to SEIRS-derived forecasts.
• Stochasticity: The execution order of daily COVID-19 actions is randomized. Random sampling determines new infections, severity assignment, visitor selection and attendance, and HCW facility/workday schedules.

4. Initialization, Parameterization, and Data Inputs

Initialization under the ODD Protocol is governed by empirical and expert-informed data sources:

• Vaccination Status Assignment:
  • HCWs: 80% vaccinated.
  • Nursing home residents: 87% vaccinated.
  • Community agents: stratified by age group and county with probabilities $P_{ac} = SR_a \times CR_{ac}$ using state- and county-level rates.
• Initial Hospitalizations and Infections:
  • Severe and critical hospitalizations are input explicitly, matching observed counts and stratified by age.
  • Length of Stay (LOS) for each hospitalized agent is drawn from a truncated normal distribution with cohort-specific parameters.
  • SEIRS submodels estimate initial exposed, infectious, and recovered populations using smoothed, case-multiplied surveillance data.
• HCW Assignment:
  • Four employment types: single-site full-/part-time, multisite, contract.
  • Target staff counts drawn from CMS payroll data, with agents matched to facilities under geographic constraints.
• Data Sources: COVID-19 cases (by county/day), vaccination counts (by county/age), CMS staffing data, and literature-derived clinical parameters.

5. Process Flow and Core Submodels

Each model day proceeds as follows:

1. Schedule base ABM location/life updates.
2. Enqueue COVID-19 actions: Recovery, New Case Generation, Nursing Home Visitation, HCW Attendance.
3. Execute all actions in random order, then advance the simulation clock.

Submodels:

• Recovery: Transition agents to Recovered on scheduled date.
• New COVID-19 Case:
  • For each county and day, potential cases are computed: $$PC_c = [(1 - Vac_c) + Vac_c (1 - V_{\text{eff}})] \times I^c_t$$, where $V_{\text{eff}}=0.24$.
  • Susceptible agents are randomly infected and assigned a severity category based on vaccination and reporting status; durations and behavioral modifications follow severity.
  • Severe/critical cases enter hospital beds (ICU or non-ICU) and are blocked from work/visitation for their LOS.
• Nursing Home Visitation: Each resident-visitor pair is evaluated daily for visit occurrence based on assigned probabilities and COVID-19 states.
• HCW Attendance: HCWs report to facilities with probability by employment type; mild COVID-19 may reduce attendance.
• SEIRS Model:
  • For each county, a deterministic SEIRS model is run with parameters (e.g., $\sigma_E=5$ days, $\sigma_I=6$ days, immunity duration 90 days, $R_0=1.25$).
  • Initial conditions are constructed from phased infection, exposure, and recovery estimates.

6. Emergence, Output Metrics, and Model Validation

The ODD Protocol specifies emergent macro-level metrics and validation patterns:

• Emergent Patterns: Daily county-level infection curves, hospital occupancy, visitation counts, and HCW attendance distributions.
• Observations and Outputs:
  • Daily infection and case outcome counts by severity.
  • Non-ICU and ICU hospital bed occupancy.
  • Nursing home visitations and HCW facility attendance.
• Validation: Model outputs are compared against empirical targets, including daily infections by county, case outcome proportions stratified by vaccination and age, total and age-distributed visitation counts, and CMS-referenced HCW ratios.

7. Integration with the Host ABM and Extensibility

The ODD Protocol as implemented for the NC MInD COVID-19 submodel is appended to a general location-movement ABM framework. The COVID-19 submodel inherits agent lifecycle logic and movement routines, with COVID-related actions queued and executed amidst base model updates. Outputs from SEIRS compartmental models feed new case events, while the main ABM’s data store (age, county, facility assignments) informs initialization and ongoing behavior (Jones et al., 2022).

This protocol-driven approach delivers modularity, detailed model specification, and comprehensive output for scenario analysis, supporting public health planning and research in resource-constrained or high-risk settings.