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ModelMeaslesMixingRiskQuarantine¶

A comprehensive epidemiological model that extends measles transmission modeling with risk-stratified quarantine strategies.

Overview¶

ModelMeaslesMixingRiskQuarantine implements a measles transmission model based on the ModelMeaslesMixing framework, with enhanced quarantine policies that vary based on exposure risk levels. This allows for targeted public health interventions that can optimize resource allocation and epidemic control.

Key Features¶

Measles-specific disease progression: Susceptible → Exposed → Prodromal → Rash → Recovered
Population mixing: Uses contact matrices to model heterogeneous mixing between population groups
Risk-stratified quarantine: Three-tier system (high/medium/low risk) with customizable durations
Enhanced detection: Detection rate parameter that activates during quarantine periods
Contact tracing: Comprehensive contact tracing with configurable success rates
Entity-based risk assessment: Risk levels determined by shared entity membership
Vaccination effects: Vaccine distribution with configurable efficacy

Disease States¶

The model includes 13 distinct states:

Susceptible - Can become infected
Exposed - Infected but not yet infectious (incubation period)
Prodromal - Infectious individuals (replaces "Infected" in standard SEIR)
Rash - Non-infectious with visible symptoms (detection occurs here)
Isolated - Detected individuals in self-isolation
Isolated Recovered - Recovered individuals still in isolation
Detected Hospitalized - Hospitalized individuals who were contact-traced
Quarantined Exposed - Exposed individuals in quarantine
Quarantined Susceptible - Susceptible individuals in quarantine
Quarantined Prodromal - Prodromal individuals in quarantine
Quarantined Recovered - Recovered individuals in quarantine
Hospitalized - Individuals requiring hospital care
Recovered - Individuals who have recovered and gained immunity

Risk Classification System¶

When the quarantine process is triggered by a detected case, contacts are classified into three risk levels:

High Risk¶

Definition: Unvaccinated agents who share entity membership with the case that triggered quarantine
Rationale: Highest transmission risk due to close, prolonged contact within same household/workplace/school
Default quarantine duration: 21 days (configurable)

Medium Risk¶

Definition: Unvaccinated agents who had contact with infected individuals but don't share entity membership
Rationale: Moderate transmission risk from community contact
Default quarantine duration: 14 days (configurable)

Low Risk¶

Definition: All other unvaccinated agents
Rationale: Lowest transmission risk, potential for community spread
Default quarantine duration: 7 days (configurable)

Note: Vaccinated agents (those with tools) are not subject to quarantine regardless of contact patterns.

Enhanced Detection¶

The model includes an enhanced detection mechanism that operates during active quarantine periods:

Detection rate quarantine: Additional parameter specifying detection probability for prodromal individuals during active quarantine
Mechanism: When any quarantine process is active, prodromal individuals have an additional chance of being detected and moved to quarantined prodromal state
Purpose: Models increased surveillance and testing during outbreak response

Parameters¶

Disease Parameters¶

Contact rate: Average number of contacts per step
Transmission rate: Probability of transmission per contact
Incubation period: Average time from exposure to becoming infectious
Prodromal period: Average duration of infectious period
Rash period: Average duration of rash symptoms
Hospitalization rate: Probability of requiring hospitalization
Hospitalization period: Average duration of hospital stay

Detection and Isolation¶

Days undetected: Average time before rash cases are detected
Isolation period: Duration of isolation for detected cases
Isolation willingness: Proportion willing to self-isolate when detected
Detection rate quarantine: Detection rate during active quarantine periods

Risk-based Quarantine¶

Quarantine period high: Duration for high-risk contacts (days)
Quarantine period medium: Duration for medium-risk contacts (days)
Quarantine period low: Duration for low-risk contacts (days)
Quarantine willingness: Proportion willing to comply with quarantine

Contact Tracing¶

Contact tracing success rate: Probability of successfully identifying contacts
Contact tracing days prior: Number of days prior to detection for tracing

Vaccination¶

Vaccination rate: Proportion of agents initially vaccinated
Vax efficacy: Vaccine effectiveness in preventing infection
Vax improved recovery: Enhanced recovery rate for vaccinated individuals

Usage Example¶

#include <epiworld/epiworld.hpp>

// Contact matrix for 3 population groups
std::vector<double> contact_matrix = {
    0.8, 0.1, 0.1,  // Group 1 mixing
    0.1, 0.8, 0.1,  // Group 2 mixing  
    0.1, 0.1, 0.8   // Group 3 mixing
};

// Create model with risk-based quarantine
epimodels::ModelMeaslesMixingRiskQuarantine<> model(
    1000,        // Population size
    0.01,        // Initial prevalence
    2.0,         // Contact rate
    0.2,         // Transmission rate
    0.9,         // Vaccination efficacy
    0.3,         // Vaccine recovery enhancement
    7.0,         // Incubation period
    4.0,         // Prodromal period
    5.0,         // Rash period
    contact_matrix, // Contact matrix
    0.2,         // Hospitalization rate
    7.0,         // Hospitalization duration  
    3.0,         // Days undetected
    21,          // Quarantine period high risk
    14,          // Quarantine period medium risk
    7,           // Quarantine period low risk
    0.8,         // Quarantine willingness
    0.8,         // Isolation willingness
    4,           // Isolation period
    0.1,         // Proportion vaccinated
    0.15,        // Detection rate during quarantine
    1.0,         // Contact tracing success rate
    4u           // Contact tracing days prior
);

// Add population entities
model.add_entity(Entity<>("Households", dist_factory<>(0, 400)));
model.add_entity(Entity<>("Schools", dist_factory<>(400, 700)));  
model.add_entity(Entity<>("Workplaces", dist_factory<>(700, 1000)));

// Set initial conditions
model.initial_states({1.0, 0.0}); // All infected start as exposed

// Run simulation
model.run(60, 123);
model.print();

Differences from Other Models¶

vs. ModelMeaslesMixing¶

Risk-stratified quarantine: Three different quarantine durations based on exposure risk
Enhanced detection: Additional detection during active quarantine periods
Entity-based risk assessment: Risk levels determined by shared entity membership
Flexible quarantine policies: Each risk level can have different quarantine duration or be disabled

vs. ModelMeaslesSchool¶

Population mixing: Supports contact matrices for heterogeneous mixing
Risk stratification: Multiple quarantine strategies rather than uniform approach
Enhanced contact tracing: Risk-based contact management
Scalability: Supports multiple population entities with different mixing patterns

Testing¶

The model includes comprehensive tests that verify: - Correct transition probabilities between all 13 states - Proper risk level assignment (high/medium/low) - Enhanced detection mechanism during quarantine periods - Different quarantine durations for different risk levels - Comparison of uniform vs. risk-stratified quarantine strategies - Population mixing functionality with multiple entities

See tests/20a-measles-mixing-risk-quarantine.cpp for test examples.

Applications¶

This model is particularly useful for:

Outbreak response planning: Comparing different quarantine strategies
Resource optimization: Allocating quarantine resources based on transmission risk
Policy evaluation: Assessing effectiveness of risk-stratified interventions
Contact tracing optimization: Understanding impact of enhanced detection during outbreaks
Vaccination strategy: Evaluating how vaccination coverage affects quarantine effectiveness

Implementation Notes¶

Risk levels are assigned dynamically when quarantine is triggered
Vaccinated agents are excluded from quarantine regardless of contact patterns
Enhanced detection only operates when at least one quarantine process is active
Quarantine durations can be set to -1 to disable quarantine for specific risk levels
The model maintains backward compatibility with uniform quarantine by setting all periods equal