Deterministic ODE Epidemic Modeling, Next Generation Matrix Analysis, and Age-Targeted Vaccine Strategy Optimization: An R-Based Dynamic Transmission Assessment of Respiratory Pathogens

This project executed a deterministic compartmental Ordinary Differential Equation (ODE) modeling and simulation study using R and the odin framework to evaluate epidemic dynamics and vaccine intervention strategies in an age-stratified population (children vs. adults). The model incorporated disease severity tiers (mild vs. severe hospitalizations), age-specific clinical profiles, and imperfect vaccine protection mechanisms.The mathematical analysis derived the Next Generation Matrix (NGM) in base R to compute age-specific transmission probabilities and solve for the basic reproduction number ($R_0$). Long-term epidemic trajectories were evaluated by relaxing the assumption of lifelong immunity, simulating endemic equilibrium dynamics under varying waning immunity durations (100 to 1,000 days). To support model calibration, a likelihood framework (Poisson/Negative Binomial) was formulated to link predicted incidence to catchment-level hospital surveillance data.Furthermore, dynamic simulation studies were conducted to optimize public health outcomes under resource-constrained conditions. By evaluating non-linear trade-offs between rollout timing, daily administration capacity, and coverage limits, the analysis identified optimal age-targeted allocation strategies for a fixed vaccine supply (70% population coverage) to maximize health impact and minimize severe hospitalizations. Finally, the project synthesized quantitative findings into decision-ready executive presentation materials and benchmarked results against published RSV age-specific hospitalization literature.