Issue: In the model formulation (Eq. 1), the quarantine compartment Mq receives individuals from the infected compartment Mi through theta_1, and releases them to the recovered compartment Mr through q. Additionally, a portion of infected devices recovers directly via theta_2.
However, the interpretation of theta = theta_1 + theta_2 is inconsistent: theta_1 and theta_2 have qualitatively different meanings (quarantine initiation vs. direct recovery), yet they are summed as a single “recovery” parameter in key derivations, including:
The Jacobian matrix linearization and eigenvalue analysis.
The calculation of the basic reproduction number R0 in Eq. (7).
The Lyapunov function formulations in both Theorem 2 and 3.
Question:
Given that theta_1 and theta_2 govern entirely different processes (quarantine entrance vs. recovery), how do the authors justify treating theta = theta_1 + theta_2 as a lumped term in derivations that assume a common outflow from the infected class Mi? Does this not violate the principle of compartmental independence and misrepresent the infection duration, potentially biasing the calculation of R0, especially since theta_1 leads to a delayed recovery (via q) rather than direct removal?