A Darwinian model for the evolution of drug resistance to long-acting PrEP during an early HIV infection

Predicting the evolution of drug resistance remains a central challenge in HIV prevention and treatment. Evolutionary trade-offs, i.e., the fitness costs of resistance, shift as drug-selective pressure changes, a complexity amplified by fluctuating drug concentrations during long-acting prophylaxis. We develop a Darwinian evolutionary game theory model of early HIV infection under bimonthly pre-exposure prophylaxis (PrEP) with long-acting cabotegravir (CAB-LA). This work introduces a mathematical framework that couples within-host viral dynamics with adaptive evolutionary processes in a time-dependent environment to study resistance evolution under long-acting PrEP. The model incorporates the dual transmission pathways of HIV: free virion spread and direct cell-to-cell transfer through virological synapses. We quantify how resistance mutations alter viral fitness across these modes. We formulate a deterministic within-host model that explicitly incorporates the dual transmission pathways and introduce continuous resistance traits governing infectivity and drug susceptibility for each pathway. T-cell parameter estimates are informed by data assimilation using acute-stage HIV infection data. CAB-LA is modeled with time-periodic pharmacokinetics-pharmacodynamics (PK/PD), yielding dynamic fitness seascapes rather than static fitness landscapes. Time-varying drug pressure introduces a trade-off between drug resistance and infectivity, driving competition among strains that favor different transmission strategies. Our results show that fluctuating drug concentrations reshape evolutionary outcomes, generating dynamic strain competition and altering the effectiveness of long-acting PrEP in blocking infection. The model reveals threshold behavior in drug robustness to mutation, identifies conditions leading to viral control, viral escape, and delayed seroconversion, and demonstrates that resistance evolution depends on both transmission pathway and initial trait configuration. These findings provide a mechanistic explanation for delayed HIV detectability observed in CAB-LA clinical trials.