Behavioral Economics of Childhood Vaccination

by Veronica Scerra

Phase 1: Cost-effectiveness analysis foundation with deterministic SEIR-V model.

Vaccination programs face a fundamental tension: while vaccines are one of the most cost-effective public health interventions, individual decision-making often leads to a less-than-optimal societal level of vaccination coverage. I embarked on this project to develop a working understanding of and an integrated epidemiological-economic-behavioral model of childhood vaccination programs, combining disease transmission dynamics with game-theoretical decision-making and cost-effectiveness analysis. At the heart of this project through the phases is the central question:

How do individual vaccination decisions, driven by perceived risks and benefits, create feedback loops with disease transmission, and what policy interventions can align individual incentives with public health goals?

I used measles as a case study for this project due to its extreme contagiousness (R₀ = 12-18), high herd immunity threshold (93-94%), and recent resurgence in areas with more pronounced vaccine hesitancy. The model quantifies both health outcomes (cases, deaths, DALYs) and economic impacts (vaccination costs, treatment costs, productivity losses) under different coverage scenarios and policy interventions.

Why SEIR-V? Model Structure and Justification

The foundation of this project is a SEIR-V compartmental model that extends the standard SEIR framework to explicitly track vaccinated individuals. This choice was made for several critical reasons:

Compartments

S (Susceptible): Individuals at risk of infection
E (Exposed): Infected but not yet infectious (latent period ~ 10 days)
I (Infected): Infectious and capable of transmitting (infectious period ~ 8 days)
R (Recovered): Naturally immune after infection
V (Vaccinated): Vaccine-induced immunity

Why include the exposed (E) compartment?

The departure from a simpler SIR model to include a separate compartment for indivudals who have been exposed, but are not yet infectious is critical for measles dynamics:

Generation time accuracy: Measles has a distinct latent period (~ 8-12 days) before infectiousness begins. A simple SIR model would underestimate the generation time by ~50%, leading to incorrect R₀ estimations and epidemic timing predictions.
Intervention timing: The latent period creates a window for post-exposure prophylaxis. SEIR captures this biological reality; SIR cannot.
Epidemic peak prediction: The E compartment delays epidemic takeoff, affecting peak timing and magnitude. For policy planning, accurate peak predictions are essential.

Why separate vaccinated (V) from recovered (R)?

Separating the immune population into V and R categories is essential for elements of economic and behavioral analysis:

Cost tracking: We need to distinguish between immunity gained through vaccination (a program cost) versus natural infection (treatment costs, DALYs lost).
Coverage monitoring: Public health targets are defined by vaccination coverage, not total immunity. Separating V allows direct comparison with policy goals.
Behavioral modeling (Phase 2): Individual vaccination decisions depend on the vaccinated proportion of the population, not total immunity. Parents ask "how many are vaccinated?" not "how many are immune?"
Efficacy modeling: Vaccine efficacy (<100%) means some vaccinated individuals remain susceptible. The V compartment can be stratified later into protected vs. unprotected.

Model equations

        SEIR-V Differential Equations: 
        
            dS/dt = νN - λS - vS - μS

            dE/dt = λS - σE - μE

            dI/dt = σE - γI - μI

            dR/dt = γI - μR

            dV/dt = vS - μV

            Where:

            • λ = β(I/N) is the force of infection

            • σ = 1/latent_period (progression rate E→I)

            • γ = 1/infectious_period (recovery rate)

            • v = vaccination rate (initially constant, later behavioral)

            • μ = natural death rate, ν = birth rate

            • β = R₀ × γ (transmission rate)

Economic Framework: WHO-Compliant CEA

For the economic analysis portion of this project, I followed WHO guidelines for economic evaluation of immunization programs, ensuring compatibility with global health decision-making frameworks.

DALY calculation (Disability-Adjusted Life Years)

DALYs combine mortality and morbidity into a single metric: DALYs = YLL + YLD

Years of Life Lost (YLL):

Deaths × (life expectancy - age at death)
Measles deaths concentrated in children → high YLL per death
US life expectancy: 78 years
Average age at death: ~5 years → 73 YLL per death
Discounted at 3% per year (WHO standard)

Years Lived with Disability (YLD):

Cases × duration × disability weight
Disability weights (from Global Burden of Disease study):
- Mild measles: 0.051 (14 days duration)
- Moderate measles: 0.133 (14 days)
- Severe measles: 0.280 (14 days)
- Long-term complications (SSPE, encephalitis): 0.400 (90 days)

Cost components

The model tracks costs from both healthcare system and societal perspectives:

ICER (Incremental Cost-Effectiveness Ratio)

Cost Category	Value (2024 USD)	Source
Direct Medical Costs
Vaccine dose	$21	CDC vaccine price list
Administration	$25	Healthcare billing codes
Outpatient treatment	$150	Mild case, clinical visit
Hospitalization	$8,000	Average per severe case
Complication treatment	$3,000	Encephalitis, SSPE
Public Health Costs
Contact tracing per case	$5,000	Public health response
Outbreak investigation	$50,000	Per outbreak event
Indirect Costs (Societal Perspective)
Caregiver time (mild)	$1,000	5 days × $200/day
Caregiver time (hospitalized)	$2,000	10 days × $200/day

WHO Cost-Effectiveness Thresholds:
• Highly cost-effective: ICER < 1× GDP per capita ($70,000/DALY in US)
• Cost-effective: ICER < 3× GDP per capita ($210,000/DALY in US)
• Not cost-effective: ICER > 3× GDP per capita

Model Validation

Before using the model for policy analysis, we validated it against theoretical predictions and empirical measles data. A fully susceptible population (no vaccination) was simulated to verify the model produces expected epidemic dynamics.

Parameter Exploration

Vaccination Baseline vs. Low Coverage Scenarios

In the low vaccination scenario, the slight gains in vaccination costs are dwarfed by the societal costs in both treatment and public health.

Sensitivity Analysis: R₀ and Vaccine Coverage Levels

Testing the model across R₀ values (12-18) and coverage levels (70-95%) reveals critical thresholds:

Validation Metric	Theoretical/Literature	Model Result
Final attack rate	93.3% (1 - 1/R₀)	100.1%
Generation time	14-21 days	18 days
Epidemic peak time	~27 days (1/γ × ln(R₀))	42 days
R₀ from growth rate	15.0 (input)	14.9 (estimated)
Peak prevalence	20-40%	36.4%

Outcome	Baseline (91%)	Low Coverage (75%)	Difference
Total cases	116,650	246,047	+129,937
Deaths	233	492	+259
Hospitalizations	23,330	49,215	+25,885
Attack rate	11.66%	24.61%	+12.95%
Peak prevalence	0.23%	5.13%	+4.9%

The model show nonlinear sensitivity to coverage near the HIT. A drop from 93% to 90% has disproportionately large effects compared to a drop from 80% to 77%, highlighting the importance of maintaining coverage above critical thresholds.

Technical Implementation

Model Structure

Lessons Learned & Design Decisions

1. SEIR vs. SIR Trade-offs

Rationale: Measles has a distinct 10-day latent period. Omitting this would cause:

Trade-off: Added computational cost is minimal (~20% slower), and biological accuracy justifies the choice.

2. Vaccination Compartment (V) Separation

3. Static vs. Dynamic Vaccination Rate

Phase 1 Limitation: Vaccination rate is constant (based on baseline coverage)

Solution:Phase 2 will implement behavioral feedback where vaccination decisions respond to disease prevalence

4. Economic Perspective Choice

5. Parameter Uncertainty

Approach: Use point estimates with sensitivity analysis rather than probabilistic simulations