Finite Prevention Windows for HIV Post-Exposure Prophylaxis: Irreversible Proviral Integration Defines Route-Specific and Population-Level Intervention Limits

Proviral integration — the molecular event that converts HIV infection from reversible to permanent— defines a finite window during which post-exposure prophylaxis (PEP) can succeed. Using a three-state absorbing Markov model parameterized on established HIV-1 kinetic constants, we prove that PEP efficacy decays monotonically to zero and derive the critical prevention window as a function of integrationkinetics rather than drug potency. This window is approximately three-fold shorter for parenteral (injection) than mucosal (sexual) exposure, yielding a parenteral tcrit of 16–28 hours versus 68–76 hours mucosally. For people who inject drugs, empirically documented structural access delays place fewer than 5% of exposures within the parenteral window, bounding expected population-level PEP efficacy below 10%—a failure determined by integration timing, not pharmacology.