Complete kinetic models are pervasive in chemistry but lacking in biological systems. We encoded the complete kinetics of infection for coxsackievirus B3 (CVB3), a compact and fast-acting RNA virus. The model consists of separable, detailed modules describing viral binding-delivery, translation-replication, and encapsidation. Specific module activities are dampened by the type I interferon response to viral double-stranded RNAs (dsRNAs), which is itself disrupted by viral proteinases. The experimentally validated kinetics uncovered that cleavability of the dsRNA transducer mitochondrial antiviral signaling protein (MAVS) becomes a stronger determinant of viral outcomes when cells receive supplemental interferon after infection. Cleavability is naturally altered in humans by a common MAVS polymorphism, which removes a proteinase-targeted site but paradoxically elevates CVB3 infectivity. These observations are reconciled with a simple nonlinear model of MAVS regulation. Modeling complete kinetics is an attainable goal for small, rapidly infecting viruses and perhaps viral pathogens more broadly. A record of this paper's transparent peer review process is included in the Supplemental information.