Global Stability and Sensitivity Analysis of n-Compartment SEI(Q1Q2…Q𝑛−4)R Model with Single Dose Vaccination

Objectives: This work develops and analyzes an extended SEI(Q₁Q₂…Qₙ₋₄)R framework that incorporates several quarantine zones, vaccination, and partial immunity to better understand epidemic behavior. Methods: The proposed framework is formulated as a nonlinear system of ordinary differential equations. The basic reproduction number is derived using the next-generation matrix method, while Lyapunov functions and LaSalle’s invariance principle are applied to establish global stability of the disease-free and endemic equilibria. Sensitivity analysis quantifies the influence of transmission, vaccination, and recovery parameters, and MATLAB (R2024a)-based simulations employing literature-supported parameter values are used for validation. Findings: The analysis establishes that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is below unity, whereas an endemic equilibrium persists when it exceeds one. Sensitivity and simulation analyses collectively validate these theoretical outcomes, identifying vaccination rate, vaccine efficacy, transmission rate, and recovery parameters as the most influential factors. Simulations of the generalized n-compartment model for n=5 and n=7 confirm that the compartmental dynamics follow the analytical stability patterns; moreover, increasing quarantine compartments effectively lowers infection peaks and accelerates recovery. Novelty: This study introduces a unified integer-order epidemic framework that generalizes to any number of compartments, allowing flexible modeling of outbreaks with multiple quarantine zones and vaccination effects. Its analytical formulation, independent of compartment count, offers a scalable foundation for evidence-based epidemic control and public health decision-making. Keywords: Epidemiology, Equilibria, Global Stability, Sensitivity Analysis, n compartmental model