Age-Structured Dynamic Transmission Model

• Age-structured dynamic transmission models stratify populations by age, tracking transitions between susceptible, infected, and recovered states.
• They incorporate age-specific contact rates, demographic adjustments, and targeted interventions to reveal transmission patterns and optimize vaccination strategies.
• Dynamic simulation and probabilistic sensitivity analysis combine epidemiology with economic evaluation to inform robust public health policy decisions.

An age structured dynamic transmission model is a class of compartmental epidemic model in which the host population is stratified by age and state variables track transitions between epidemiological compartments (such as susceptible, infected, recovered) within each age group over time. These models are foundational in infectious disease epidemiology for understanding how transmission dynamics, clinical outcomes, and intervention impacts vary over the lifespan, and are especially relevant for pathogens with strong age-dependent susceptibility, infectiousness, or severity.

1. Model Formulation and Structure

Age structured dynamic transmission models generalize traditional compartmental models like SIR and SEIR by replacing simple population totals with age-grouped compartments. Population is divided into mutually exclusive age bands (e.g., 0–19, 20–39, 40–59, 60+), each represented with parallel sets of compartmental variables. Infections, progressions, recoveries, and transitions due to demography (aging, birth, death) are modeled as flows between these compartments.

For each age group $a$, let $S_a$, $I_a$, and $R_a$ denote susceptible, infectious, and recovered individuals, respectively, at time $t$. The force of infection $\lambda_a(t)$ for age group $a$ is typically given by

$$\lambda_a(t) = \sum_b \beta_{a b} \frac{I_b(t)}{N_b(t)}$$

where $\beta_{a b}$ encodes the transmission matrix reflecting age-specific contact rates, and $N_b(t)$ is the total population in group $b$. Demographic rates (birth, death, aging) and intervention factors (e.g., age-targeted vaccination) are incorporated as group-specific transition terms.

2. Calibration and Dynamic Simulation

Parameterization and calibration are critical to ensure age structured transmission models reflect real-world epidemiology. Direct calibration to longitudinal or seroprevalence data is standard, often constrained by demographic data and observed case notifications stratified by age. The model described in "Cost-Effectiveness of Adult Hepatitis A Vaccination Strategies in Korea Under an Aging Susceptibility Profile" (Lim et al., 20 Jan 2026) is calibrated to national Korean data, capturing historic trends in hepatitis A susceptibility, incidence, and vaccination coverage by age.

Dynamic simulation propagates the model forward over multi-decade horizons, accounting for the evolving demography and immunity profile across cohorts. Intervention scenarios can be encoded via exogenous vaccination rates or allocation schemes, with outcomes (e.g., cases, hospitalizations, deaths, DALYs) tallied by age and time.

3. Integration with Economic Evaluation

A central application of age structured dynamic transmission models is to inform health-economic evaluations, including calculation of incremental cost-effectiveness ratios (ICERs), net monetary benefit (NMB), and cost-effectiveness acceptability curves (CEACs). In (Lim et al., 20 Jan 2026), model-predicted disease events and vaccination metrics by age and time are input into lifetime horizon economic analyses, quantifying discounted costs and health benefits (DALYs averted) for each candidate strategy.

Probabilistic sensitivity analysis (PSA) is conducted by repeatedly simulating the model under joint uncertainty in epidemiological, cost, and utility parameters. For each simulation draw, model outputs propagate through the economic analysis, providing a joint distribution of cost and effectiveness outcomes conditional on the underlying transmission dynamics and age structure.

4. Example: Optimization of Vaccination Strategies

In the context of Korean hepatitis A control, three age-targeted adult vaccination strategies were evaluated:

• S1: Vaccinate 20–39 year olds.
• S2: Vaccinate 40–59 year olds (with serotesting).
• S3: Vaccinate 20–59 year olds.

An age structured dynamic model characterized the evolving risk landscape driven by an aging susceptible cohort and computed dynamically feasible vaccination allocation trajectories using optimal control. Outputs include discounted lifetime costs, DALYs, and infection outcomes for each strategy (Lim et al., 20 Jan 2026).

Dynamic simulation allows comparative assessment across target groups, capturing both direct and indirect (herd) effects and reflecting the future distribution of severe outcomes by age as demographic shifts occur.

5. Uncertainty Characterization and Decision Support

The joint epidemiological and economic uncertainty is summarized through cost-effectiveness acceptability curves (CEACs). In the base case, for each Monte Carlo PSA draw, the age structured model is run to generate lifetime outcomes for the baseline and each intervention. The NMB at threshold $\lambda$ is computed:

$$\mathrm{NMB}_i(\lambda) = \lambda\,\Delta E_i - \Delta C_i$$

where $\Delta E_i$ is the incremental DALYs averted and $\Delta C_i$ the incremental cost for strategy $i$ versus baseline.

The CEAC for strategy $i$ at $\lambda$ is

$$\mathrm{CEAC}_i(\lambda) = \Pr[\mathrm{NMB}_i(\lambda) = \max_{j} \mathrm{NMB}_j(\lambda)]$$

i.e., the fraction of draws in which a given strategy is optimal under uncertainty. This approach quantifies the robustness of ranking across WTP thresholds: in (Lim et al., 20 Jan 2026), S2 dominates across most plausible $\lambda$ values, indicating consistent cost-effectiveness over uncertainty in both model structure and parameters.

6. Interpretation, Policy Implications, and Limitations

Age structured dynamic transmission models support policy decisions by integrating heterogeneity in risk, immunity, and outcome severity as a function of age. In the analyzed Korean context, this approach reveals that, although broader adult vaccination (S3) achieves maximum DALY reduction, the more focused S2 strategy offers superior cost-effectiveness given demographic and economic constraints. This conclusion is robust to a wide range of plausible inputs and is strengthened by the joint propagation of uncertainty in both the epidemiological and cost-effectiveness components (Lim et al., 20 Jan 2026).

A plausible implication is that such models can reveal counterintuitive optimal priorities under dynamic demographic transition, which static or unstructured analyses may miss.

Limitations include sensitivity to structural modeling assumptions (e.g., contact matrices, external force-of-infection), data quality for age-stratified parameters, and the need for extensive computational resources for high-dimensional PSA. Nevertheless, the ability to propagate age-specific interventions realistically through time makes age structured dynamic models central to resource allocation for vaccination and other public health strategies under demographic change.