Alex Viguerie

We present a two-stage methodology for reconstructing Alzheimer’s disease (AD) incidence over time using ensemble Kalman inversion (EKI) applied to mortality data. In the first stage, we use EKI to infer temporal trends in all-cause and Alzheimer’s-specific mortality by fitting an age-structured demographic model to observed death counts. This yields posterior estimates of evolving population structure and age-specific AD mortality rates. In the second stage, we apply a back-calculation procedure that uses these estimates, along with the hazard of AD-related death following disease onset, to infer time- and age-specific incidence rates. This reverse-inference framework enables the reconstruction of latent disease dynamics in the absence of direct incidence surveillance. By integrating demographic structure, disease-specific hazards, and observed mortality into a coherent inferential pipeline, our approach offers a principled and flexible tool for monitoring chronic disease trends and estimating historical disease burden. Relevance to Life Sciences.: 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. Mathematical Content.: 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. The underlying inverse problem is formulated with mathematical rigor, and its well-posedness is formally established. By leveraging an ensemble of plausible population reconstructions—each consistent with observed mortality patterns—we obtain probabilistic estimates of incidence that are not only dynamically consistent but also accompanied by principled uncertainty quantification.

The advent of antiretroviral therapy (ART) has led to substantial increases in life expectancy among persons with diagnosed HIV (PWDH), and in turn, an increasingly older population. This represents a public health challenge, as older PWDH are more susceptible to age-related health morbidities compared to the general population. In this study, we triangulate diverse data sources to reconstruct the Italian PWDH age structure over the past decade to better-understand recent trends, and provide demographic projections through 2035. We find that the PWDH population grew from approximately 112,000 persons in 2012, to 140,000 in 2024, and forecasted to reach 155,000 by 2035. This is primarily driven by decreased PWDH mortality, with such decreases forecast to continue. Persons over 60, estimated as 8.6% of the PWDH population in 2012, had increased to over 20% by 2020, and are projected to reach 47.2% by 2035. By 2030, over 10% of PWDH in Italy are projected to be over 75, compared to less than 1% in 2012. Our results demonstrate that the Italian HIV care infrastructure must prepare for a dramatic shift from managing a predominantly young-adult disease to caring for a majority-elderly population within the next decade, representing an unprecedented transformation in the nature and scope of required services.

Partial differential equation (PDE) models for infectious diseases, while less common than their ordinary differential equation (ODE) counterparts, have found successful applications for many years. Such models are typically of reaction-diffusion type, and model spatial propagation as a diffusive process. However, given the complex nature of human mobility, such models are limited in their ability to describe airborne infectious diseases in human populations. Recent work has advocated for the inclusion of an additional chemotaxis-type term as an alternative; spatial propagation of infection fronts is assumed additionally to flow from low-to-high concentrations of susceptible populations. The present work extends the study of such models by providing an epidemiologically interpretable analysis, directly connecting model behavior to information readily available to policymakers. In particular, we derive a spatially-aware basic reproduction number, which accounts for spatial heterogeneity in population density. Furthermore, we discuss several important aspects concerning the numerical solution of the model, including the introduction of a stabilization scheme. Finally, we perform a series of simulation studies in the Italian region of Lombardy (severely affected by the COVID-19 outbreak in 2020) and in the US state of Georgia, in which we demonstrate the model's potential to better capture important spatiotemporal dynamics observed in real-world data compared to pure reaction-diffusion models.

Due to the widespread availability of effective antiretroviral therapy regimens, average lifespans of persons with HIV (PWH) in the United States have increased significantly in recent decades. In turn, the demographic profile of PWH has shifted. Older persons comprise an ever-increasing percentage of PWH, with this percentage expected to further increase in the coming years. This has profound implications for HIV treatment and care, as significant resources are required not only to manage HIV itself, but also associated age-related comorbidities and health conditions that occur in ageing PWH. Effective management of these challenges in the coming years requires accurate modelling of the PWH age structure. In the present work, we introduce several novel mathematical approaches related to this problem. We present a workflow combining a PDE model for the PWH population age structure, where publicly available HIV surveillance data are assimilated using the Ensemble Kalman Inversion algorithm. This procedure allows us to rigorously reconstruct the age-dependent mortality trends for PWH over the last several decades. To project future trends, we introduce and analyse a novel variant of the dynamic mode decomposition (DMD), nonnegative DMD. We show that nonnegative DMD provides physically consistent projections of mortality and HIV diagnosis while remaining purely data-driven, and not requiring additional assumptions. We then combine these elements to provide forecasts for future trends in PWDH mortality and demographic evolution in the coming years.

Background: People with diagnosed HIV (PWDH) live longer but have increased co-morbidities than peers without HIV and premature ageing. In 2021, 54% of United States PWDH were aged ≥50 years. PWDH age distribution projections beyond 2030 are needed to plan future HIV and ageing care. Methods: Our life table-based model used 2020–2021 Centers for Disease Control and Prevention National HIV Surveillance System data to project PWDH age distributions from 2021–2040 across three modeled scenarios, varying annual percentage change (APC) in HIV diagnoses (new infections proxy) and PWDH mortality rate. Results: The median age of PWDH increased from 51 years (2021) to 55–60 years (2040) when diagnoses decreased. Numbers of older PWDH increased across racial/ethnic groups and regions, regardless of decreasing or increasing diagnoses or reducing mortality. Reducing diagnoses 90% by 2040 with reduced mortality estimated 75% (695 912) of PWDH would be aged ≥50 years, 42% (388 639) aged ≥65 years, and 20% (190 600) aged ≥75 years. Extending −3% APC reductions in diagnoses projected 64% (670 977) aged ≥50 years, 33% (350 025) aged ≥65 years, and 16% (168 139) aged ≥75 years. Modestly increasing diagnoses projected 53% (761 194) aged ≥50 years, 26% (371 244) aged ≥65 years, and 12% (171 233) aged ≥75 years. Across scenarios, the number of PWDH aged ≥50, ≥65, and ≥75 years, respectively, increased 18%–34%, 144%–171%, and 565%–654%. Conclusions: By 2040, the estimated number of older PWDH will increase substantially, regardless of decreasing or increasing HIV diagnoses. The healthcare sector must prepare now to ensure future ageing-related care needs of PWDH are met.

We present a two-stage methodology for reconstructing Alzheimer's disease (AD) incidence over time using ensemble Kalman inversion (EKI) applied to mortality data. In the first stage, we use EKI to infer temporal trends in all-cause and Alzheimer's-specific mortality by fitting an age-structured demographic model to observed death counts. This yields posterior estimates of evolving population structure and age-specific AD mortality rates. In the second stage, we apply a back-calculation procedure that uses these estimates, along with the hazard of AD-related death following disease onset, to infer time- and age-specific incidence rates. This reverse-inference framework enables the reconstruction of latent disease dynamics in the absence of direct incidence surveillance. By integrating demographic structure, disease-specific hazards, and observed mortality into a coherent inferential pipeline, our approach offers a principled and flexible tool for monitoring chronic disease trends and estimating historical disease burden.

Background: High HIV transmission persists in many U.S. jurisdictions despite prevention efforts. HIV self-testing offers a means to overcome barriers associated with routine laboratory-based testing but carries a risk of increasing incidence if replacement effects reduce overall test sensitivity. Methods: A linearized four-compartment HIV transmission model was applied to 38 Ending the HIV Epidemic (EHE) priority jurisdictions. A threshold testing level was defined to counterbalance potential negative effects from reduced self-test sensitivity. Both the percentage of self-tests and the overall testing rate were varied to quantify 10-year changes in HIV incidence. Results: Substantial heterogeneity emerged across districts. Incidence reductions exceeded 5 percent in some areas, while others saw only minor effects. Jurisdictions with higher baseline testing displayed an elevated risk of increased incidence from substitution of laboratory-based testing with self-tests. In contrast, a derived Awareness Reproduction Number, capturing transmissions attributable to undiagnosed infection, strongly correlated with the magnitude of possible incidence declines. Conclusions: Local epidemiological context is pivotal in determining the risks and benefits of HIV self-testing. Jurisdictions with robust testing systems may face a greater likelihood of inadvertently raising incidence, whereas those with a high number of individuals stand to achieve notable transmission reductions. Tailoring self-testing strategies based on jurisdiction-specific conditions can maximize public health benefits while minimizing unintended consequences.

Due to the widespread availability of effective antiretroviral therapy (ART) regimens, average lifespans of persons with HIV (PWH) in the United States have increased significantly in recent decades. In turn, the demographic profile of PWH has shifted. Older persons comprise an ever-increasing percentage of PWH, with this percentage expected to further increase in the coming years. This has profound implications for HIV treatment and care, as significant resources are required not only to manage HIV itself, but associated age-related comorbidities and health conditions that occur in aging PWH. Effective management of these challenges in the coming years requires accurate modeling of the PWH age structure. In the present work, we introduce several novel mathematical approaches related to this problem. We present a workflow combining a PDE model for the PWH population age structure, into which publicly-available HIV surveillance data is assimilated using the Ensemble Kalman Inversion (EKI) algorithm. This procedure allows us to rigorously reconstruct the age-dependent mortality trends for PWH over the last several decades. To project future trends, we introduce and analyze a novel variant of the Dynamic Mode Decomposition (DMD), nonnegative DMD. We show that nonnegative DMD provides physically-consistent projections of mortality and HIV diagnosis while remaining purely data-driven, and not requiring additional assumptions. We then combine these elements to provide forecasts for future trends in PWDH mortality and demographic evolution in the coming years.

Background: Despite progress in HIV prevention and treatment, resulting in overall incidence reductions in the United States, large racial/ethnic (r/e) disparities in HIV incidence remain due to stigma, discrimination, racism, poverty, and other social and structural factors. Setting: We used the HIV Optimization and Prevention Economics (HOPE) model to analyze which intervention strategies provide the most effective path towards eliminating r/e disparities in HIV incidence. Methods: We considered four intervention scenarios for 2023-2035, which focused on eliminating r/e disparities by 2027 in the HIV care continuum only, HIV prevention services only, both continuum and prevention services, and a final scenario where prevention and care levels for Black and Hispanic/Latino were set to maximum feasible levels. The primary outcome is the incidence-rate-ratio (IRR) for Black and Hispanic/Latino populations compared to Other populations (of whom 89% are White) with the goal of IRRs ≤ 1 by 2035. Results: All scenarios reduced IRRs but only Maximum Feasible eliminated HIV incidence disparities by 2035, with respective IRRs of 0.9 and 1.1 among the Black and Hispanic/Latino populations, compared to 6.5 and 4.1 in the baseline scenario. Continuum-only was more effective at reducing disparities (2035 IRRs of 4.7 for Black and 3.1 for Hispanic/Latino populations) than Prevention-only (6.1 and 3.7 respectively). Conclusions: With no prioritized changes, our simulation showed that r/e disparities in HIV incidence persist through 2035. Elimination of r/e incidence disparities by 2035 is only possible if maximum HIV prevention and care levels for Black and Hispanic/Latino populations can be realized by 2027.