Epidemic incidence reflects both transmission dynamics and adaptive human behavior, yet these mechanisms may be difficult to distinguish from aggregate case data alone. We calibrated four susceptible--infected--recovered (SIR) specifications to weekly confirmed COVID-19 incidence in New York City from June to December 2020, comparing a single continuous SIR trajectory, a wave-initialized SIR model, and two adaptive-behavior models with either shared or wave-specific transmission. Inference was performed using rejection Approximate Bayesian Computation (ABC), and in-sample reconstruction was assessed using root mean squared error (RMSE) and the weighted interval score (WIS). Reinitializing the epidemic state by wave produced the largest structural improvement over the continuous SIR trajectory, reducing mean-based RMSE by 48.6\% and WIS by 17.6\%. Adding delayed prevalence-dependent behavioral adaptation with shared transmission further reduced mean-based RMSE by 23.4\%, but yielded essentially unchanged WIS relative to the wave-initialized SIR model. Allowing transmission to vary by wave did not provide a consistent additional advantage and produced strongly asymmetric posterior-simulation trajectories. Behavioral sensitivity, response midpoint, and delay remained only weakly to partially identified. The clearest posterior structure was a negative association between transmission intensity and the behavioral midpoint, indicating that higher transmission could be compensated by behavioral responses activated at lower prevalence. Sensitivity to ordered behavioral priors further showed that reconstruction and behavioral inference depend materially on structural prior assumptions. These results suggest that adaptive mechanisms can improve multi-wave incidence reconstruction, while aggregate incidence alone is insufficient to sharply separate transmission from behavioral adaptation.

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