The effects of HIV self-testing on HIV incidence and awareness of status among men who have sex with men in the United States: Insights from a novel compartmental model

The paper’s Supplement A derives the linearized infected subsystem, specifies F and V with only the first row of F nonzero, and computes Rt as the spectral radius of the next‑generation matrix NV^{-1} (their N = F), yielding exactly the closed‑form expression stated in Proposition 2 at Σ = Σ0. The displayed V^{-1} and the resulting Rt match the candidate’s formula and method; the candidate’s argument (rank‑one K = F V^{-1}, so ρ(K) = K11) is the same idea implemented slightly more explicitly. The paper’s displayed Rt assumes equal detection hazards across undiagnosed stages (ϕ̃a = ϕ̃u = ϕ̃s = ϕ̃), while the general unequal‑ϕ̃i expression is exactly what the candidate derives before specializing. See the paper’s F and V (A2–A3), linearized system (A4), and Proposition 2 statement and proof giving V^{-1} and Rt.