Mathematical model for an infectious disease with quarantine

This article presents a novel compartmental mathematical model for an infectious disease that uniquely distinguishes susceptible individuals into quarantined and non-quarantined groups, while explicitly capturing dynamic transitions between these compartments. Unlike traditional models, ours integrates the combined effects of quarantine effectiveness and population mobility on disease transmission dynamics. We rigorously define the biologically feasible region and prove its positive invariance, ensuring model consistency. Using the next-generation matrix method, we derive a precise expression for the basic reproduction number (\mathcal{R}_۰). Our analytical contributions include establishing both local and global stability of the disease-free equilibrium for \mathcal{R}_۰ < ۱, and, notably, developing a novel Lyapunov function to prove the global asymptotic stability of the endemic equilibrium when \mathcal{R}_۰ > ۱. Through comprehensive numerical simulations, we validate the theoretical results and provide new insights into the critical role of quarantine measures in epidemic control. These findings offer valuable guidance for designing more effective public health intervention strategies.

کلیدواژه ها:

Infectious diseases‎ ، ‎Local stability‎ ، Global stability‎ ، ‎Reproduction number‎ ، ‎Lyapunov function