A review of commonly used compartmental models in epidemiology

The paper, a review, correctly states the standard framework: R0 is computed as the spectral radius of FV^{-1}, FDE/EE are defined and their local stability is assessed via linearization and Routh–Hurwitz, with global stability sketched via Lyapunov functions; it also summarizes numerical methods per model class. These elements appear explicitly in the paper’s overview of the common background and examples (definitions of FDE/EE and the R0 construction; emphasis on local stability via characteristic roots/Routh–Hurwitz; and numerical method choices) , with concrete PDE examples aligning with the R0-threshold and Lyapunov-based global stability narrative . The candidate model solution is largely consistent with this, but contains a concrete error: its fourth-order Routh–Hurwitz conditions omit the necessary Δ2 inequality (a1 a2 > a3), rendering that part incorrect. It also introduces additional assumptions (e.g., a block-triangular Jacobian with a Hurwitz uninfected block) that the paper does not spell out, although these are standard in the cited framework.