A Two-Compartment Antiviral Pulse-Dosing Model Under Resistance Evolution: MSW Mechanisms, Numerical Optimization, and Finite-Time Stability Analysis

Antiviral pulse dosing is shaped by discrete dosing events, two-compartment pharmacokinetics, nonlinear pharmacodynamics, and resistance evolution. To characterize sustained suppression, resistance accumulation, and risk-cost tradeoffs within a unified framework, this study formulates a two-compartment pharmacokinetic-viral dynamic pulse-dosing model with competition between drug-sensitive and drug-resistant strains. Nonlinear metabolic terms, safety constraints, and a mutant selection window (MSW) residence metric are incorporated. Rather than merely superimposing standard logistic growth, Emax pharmacodynamics, and Dirac-delta impulses, the proposed framework couples cross-compartment exposure, MSW residence, resistance ratio feedback, and finite-time stability diagnostics in a discrete-control setting. Pontryagin’s minimum principle is used to derive marginal optimality conditions for impulsive dosing, whereas the numerical implementation adopts a safety-constrained grid search over a finite set of candidate dose intensities. Scenario simulations for SARS-CoV-2 and HIV suggest that, under the assumed mechanisms and parameter ranges examined, high-intensity or high-frequency dosing may improve short-term viral suppression but may also increase MSW crossings and tail residence, thereby amplifying resistance accumulation and finite-time sensitivity risk. The stratified results should therefore be interpreted as a theoretical sensitivity analysis rather than as direct clinical prescribing guidance. The framework may provide a basis for subsequent individualized PK/PD calibration and resistance monitoring.