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Infectious disease treatments, both pharmaceutical and vaccine, face three universal challenges: the difficulty of targeting treatments to high-risk 'superspreader' populations who drive the great majority of disease spread, behavioral barriers in the host population (such as poor compliance and risk disinhibition), and the evolution of pathogen resistance. Here, we describe a proposed intervention that would overcome these challenges by capitalizing upon Therapeutic Interfering Particles (TIPs) that are engineered to replicate conditionally in the presence of the pathogen and spread between individuals--analogous to 'transmissible immunization' that occurs with live-attenuated vaccines (but without the potential for reversion to virulence). Building on analyses of HIV field data from sub-Saharan Africa, we construct a multi-scale model, beginning at the single-cell level, to predict the effect of TIPs on individual patient viral loads and ultimately population-level disease prevalence. Our results show that a TIP, engineered with properties based on a recent HIV gene-therapy trial, could stably lower HIV/AIDS prevalence by ∼30-fold within 50 years and could complement current therapies. In contrast, optimistic antiretroviral therapy or vaccination campaigns alone could only lower HIV/AIDS prevalence by <2-fold over 50 years. The TIP's efficacy arises from its exploitation of the same risk factors as the pathogen, allowing it to autonomously penetrate superspreader populations, maintain efficacy despite behavioral disinhibition, and limit viral resistance. While demonstrated here for HIV, the TIP concept could apply broadly to many viral infectious diseases and would represent a new paradigm for disease control, away from pathogen eradication but toward robust disease suppression.