SARS-CoV-2 spread and quarantine fatigue: a theoretical model

The paper formulates a two-group SIR with one-way H→M transfers activated after a tolerance time T and reports, via simulations, (i) two peaks in total prevalence when T>0, (ii) qualitative comparative statics for βH, βM, f, T, and (iii) a single peak when T=0 for their chosen benchmark parameters. However, it provides no mathematical proofs and phrases the T=0 result only as an empirical observation for that parameter set, not a theorem. The candidate model gives rigorous arguments: (A) a constructive existence proof of two peaks with the second after T; (B) an analytic counterexample showing that two peaks can also occur when T=0 (contradicting any generalized reading of the paper’s T=0 claim); and (C) local comparative statics with clear sign conclusions, all consistent with the paper’s qualitative trends. Hence the paper’s claims are empirically supported but theoretically incomplete, while the model’s solution is correct and sharper, including a counterexample that clarifies the limits of the T=0 observation. Key equations and claims from the paper (model definition, figures showing two peaks, and the T=0 single-peak observation) are confirmed in the PDF itself.