Recent Advances in Numerical and Data-Driven Methods in Public Health

This presentation will cover recent developments in numerical and data-driven methods in public health, with a focus on two key areas:
 
 - Input-output reduced order modeling for parameter space reduction.  
Mathematical models have become indispensable for planning, evaluating, and implementing public health interventions. These models often require detailed information across multiple population strata, but this level of detail introduces challenges, including computational costs and a high number of input parameters, which complicates effective study design. To address these issues, we propose a novel technique to reduce the dimensionality of the model’s input space, simplifying model-informed intervention planning. Our method applies a dimension reduction technique to the model output space and develops a process to map the reduced output back to a corresponding input space vector, thereby reducing its dimensionality. We demonstrate this approach using the HIV Optimization and Prevention Economics (HOPE) model, providing proof of concept.

- Aging Among Persons with HIV: Developing Numerical and Data-Driven Tools for a Growing Health Concern.
The development of effective antiretroviral therapy (ART) has transformed HIV from a fatal diagnosis to a manageable chronic condition, extending lifespans among persons with HIV (PWH) in developed countries to near general population levels. Consequently, the PWH demographic has shifted dramatically, with those over 55 increasing from 16% in 2008 to 45% in 2022. HIV care now involves not only managing the virus but also addressing age-related comorbidities, which present at higher rates and earlier ages in PWH. Additionally, long-term ART use introduces its own health complications.

This talk will present new mathematical tools to project the evolving age structure of PWH and the burden of age-related comorbidities. We introduce a novel Inverse Ensemble Kalman Filter (InvEnKF) workflow to reconstruct the evolution of age-dependent mortality among PWH over the past two decades. For future mortality forecasts, we develop and apply a variant of Dynamic Mode Decomposition (DMD), specifically non-negative DMD (nnDMD), and explore its mathematical properties. Unlike other methods, nnDMD generates forecasts solely from data without additional assumptions. These tools are integrated into a broader modeling framework to forecast the demographic evolution of the U.S. PWH population in the coming years.