Mathematical Modeling of HIV/AIDS in the Era of Combined Prevention, Social Stigma, and Intelligent Solvers: A Critical Review and Reproducibility Framework

Source abstract

Mathematical models of HIV/AIDS have moved from compact threshold systems to multilayer frameworks coupling infection stage, testing, antiretroviral therapy (ART), viral suppression, preexposure prophylaxis (PrEP), adherence, behavior, and stigma. At the same time, neural surrogates and scientific machine learning are increasingly used to approximate model trajectories and accelerate simulation. The two developments are often assessed separately, and numerical accuracy is sometimes mistaken for epidemiological validity. This review provides a unified mathematical account of the field. We organize deterministic HIV models by biological resolution, intervention mechanism, social structure, and computational purpose; derive a general infected-subsystem representation that contains many published compartmental models as special cases; and compare the assumptions underlying reproduction numbers, local and global stability, bifurcation, sensitivity, identifiability, and optimal control. Particular attention is given to the mathematical representation of stigma, because its effects may enter acquisition, diagnosis, disclosure, linkage to care, adherence, or loss to follow-up and therefore cannot generally be represented by one transition rate. We further review classical time integrators, Bayesian- regularized neural networks, recurrent networks, and physics-informed methods. A table-only benchmark, reconstructed from an eight-state stigma–prevention– treatment model, illustrates why interpolation, chronological extrapolation, repeated initialization, scale-aware errors, positivity, and residual checks must be reported together. The synthesis yields a reproducibility checklist and a decision framework linking scientific questions to appropriate model and solver classes. The principal conclusion is that credible HIV modeling requires three simultaneous forms of validation: structural validation of the transmission mechanism, inferential validation against identifiable data, and numerical validation of the computational method. This framework clarifies what neural surrogates can establish, what they cannot establish, and how future hybrid models can become more transparent, comparable, and decision relevant.