Optimal Control of Joint Multi-Virus Infection and Information Spreading

Both the paper and the model correctly set up the PMP and the separable pointwise minimization/maximization in the controls, yielding endpoint (bang) solutions with threshold tests for concave h_i and first-order implicit characterizations for strictly convex h_i. However, both rely on an unproven monotonicity of the switching functions (φ_i or c_i) to conclude at-most-one crossing and, more strongly, common switching times across all three controls. The paper’s proof of monotonicity is internally inconsistent and does not establish the claimed property; the model repeats the same assumption and additionally asserts common switching times and a common interior α(t) without sufficient conditions. Hence, both arguments are incomplete.