Although age-related chronic disease accounts for a large, and growing, share of healthcare spending in developed countries, the quantitative modeling of such diseases at the population level remains underdeveloped. Progress in this area requires understanding age-dependent, time-varying epidemiological processes, such as mortality, incidence, and risk, that are latent, noisy, and not directly observable in general. Furthermore, these dynamics are driven by temporal, age-related, and demographic effects, and understanding the relative importance of each is important. This talk presents computational methods combining PDE-based modeling, data assimilation, and data-driven methods to improve chronic disease forecasting and surveillance. We integrate age-structured demographic models with ensemble-based data assimilation to form a forward-inverse modeling pipeline that combines mechanistic structure with data-driven inference. Historical dynamics are reconstructed using inverse Ensemble Kalman filtering, while future evolution is learned directly from data through operator-based methods. In particular, we introduce non-negative Dynamic Mode Decomposition as a constraint-preserving, assumption-light approach for learning demographic evolution operators without prescribing parametric functional forms. We then employ the computational pipeline to project the demographic structure of persons with HIV (PWH) in the United States and Italy over the coming years. In surveillance applications, latent age-specific incidence and risk often cannot be directly observed, and must be inferred indirectly from aggregate population observations, such as death certificates. To address such cases, we develop a demographically-aware inversion procedure for risk and incidence estimation. By embedding this inference within the population dynamics, the framework enables the reconstruction of latent aging trajectories that are otherwise inaccessible. Furthermore, this allows us to separate trends driven primarily by demographics from those caused by changes in risk over time – of substantial importance in forecasting. We apply the computational pipeline to reconstruct Alzheimer’s disease (AD) and alcoholic liver disease (ALD) incidence and risk dynamics in the US, showcasing its utility and flexibility.