Data-Driven Multiscale Analysis of the HIV Epidemic in the USA: Structural and Practical Identifiability Across Epidemiological Scales

We present a multiscale model of HIV that couples within-host viral dynamics with population-level transmission to capture the interplay between individual infection and epidemic spread. The model is structured by treatment age, allowing viral load to influence both infectiousness and progression to AIDS. The model is fitted using both clinical data (viral load and target cell counts of treated individuals) and epidemiological data (HIV incidence, diagnoses, and AIDS classifications). We derive the basic reproduction number and establish threshold conditions for the existence and stability of disease-free and endemic equilibria. Structural identifiability is assessed via input-output equations, showing that the multiscale model is identifiable when the initial number of treated individuals is set to zero and the AIDS death rate is assumed known. Parameters are estimated sequentially: within-host parameters are obtained via nonlinear mixed-effects modeling of clinical data, followed by estimation of population-level parameters using CDC surveillance data. Numerical simulations are performed using a finite-difference scheme with Picard iteration, and practical identifiability is evaluated via Monte Carlo simulations across varying noise levels. Results indicate that current strategies are unlikely to meet the 2030 targets, while increasing diagnosis rates and reducing transmission from diagnosed individuals could significantly alter epidemic trajectories. These findings highlight the importance of multiscale modeling and identifiability in informing effective HIV intervention strategies.