Where and when

speaker: Alex Viguerie
affiliation: Università degli Studi di Urbino Carlo Bo
date: Wednesday, December 3, 2025 – 3.30 pm (Italian time)
venue: Genoa (Italy), Polo Valletta Puggia – Università di Genova: DIBRIS-DIMA (room 322)
link: Google Meet

Mathematical and Data-Driven Approaches to Aging in Chronic Disease: Applications to HIV and Alzheimer’s Disease

abstract: Despite comprising an ever-increasing share of healthcare spending in developed countries, age-related chronic disease remains an underdeveloped research area in applied mathematics. This talk focuses on two recent developments in this space: aging among persons with HIV, and the estimation of Alzheimer’s disease (AD) risk and incidence from population data.

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.

Estimating Alzheimer’s Disease Risk and Incidence: A Forward–Inverse Demographic Framework

Despite the importance of age-dependent AD incidence and risk dynamics over time for policymakers and public health practitioners, such information is not readily available, as direct observation is difficult or impossible. This framework thus offers a robust, extensible approach for estimating latent epidemiological quantities of public health significance, especially in contexts where direct measurement is infeasible.

The proposed framework integrates data assimilation with a dynamic demographic model governed by an age-structured partial differential equation, alongside a deconvolution-based back-calculation method, to infer age-specific incidence and risk trajectories of Alzheimer's disease over time. This synergistic combination enables the assimilation of noisy, incomplete population-level data into a coherent forward-inverse modeling pipeline. By leveraging an ensemble of plausible population reconstructions, we obtain probabilistic estimates of incidence that are not only dynamically consistent but also accompanied by principled uncertainty quantification.