Cholera Transmission Dynamics with Sanitation Control Measures

The paper’s model, equilibrium, and threshold statements exactly match the candidate’s results: the DFE is (Λ/(µ+ν), 0, νΛ/(µ(µ+ν)), 0) as derived in the paper’s Equilibria section, and the paper’s formula for R0 coincides term-by-term with the candidate’s next-generation calculation, including the Monod derivative contribution at W=0 and the θ/σ linkage through the environment. Local stability is asserted to follow the classic threshold: DFE stable if R0<1 and unstable if R0>1. The paper arrives at R0 via linearization and ratio-of-inflow/ removal reasoning and mentions the Jacobian-based stability criterion; the candidate provides a fully explicit next-generation matrix (F,V), block Jacobian, and determinant/trace test. Hence, both are correct; the proofs differ in presentation detail and formalism. Model equations and interventions are consistent with the paper’s system (1) and assumptions, including β2(W)=βmax W/(k+W) and controls ϵh, ϵw, ν. See the model formulation and assumptions , the DFE derivation , the explicit R0 expression and DFE Jacobian discussion , and the stated R0-threshold stability conclusion .