Investigating the Basin of Attraction and Sensitivity of SIQR-QS-QI Model - Jha, Sarita; Mandal, Prabhat Kumar; Jha, Govind Kumar; Roy, Chandra (Communications in Mathematics and Applications, 2026)
This study presents the creation and analysis of a deterministic SIQR epidemic model that depicts how susceptible and infectious individuals interact with others who have been quarantined. The model demonstrates the key structure of disease transmission during quarantine processing. The stability properties of both the disease-free equilibrium (DFE) and endemic equilibrium (EE) were investigated using linearization via the Jacobian matrix and nonlinear analysis through Lyapunov’s method. A sensitivity study of the reproductive number \((R_0)\) was performed to determine the most influential parameters affecting disease dynamics and control. We additionally provide a guaranteed estimate of the basin of attraction for the EE, which characterizes the initial conditions that result in the persistence of the disease. Numerical simulations are used to validate theoretical conclusions and explain how critical parameters affect disease progression. This study provides valuable insights that can support the enhancement of public health strategies and refinement of quarantine protocols.
Keywords: Equilibrium point; Stability; Reproduction number; Lyapunov function; Sensitivity analysis; Domain of attraction