基于潜伏者隔离的传染病模型演化分析

Evolutionary Analysis of Infectious Disease Models Based on Isolating Latent Individuals

摘要: 本文构建了一类引入潜伏者隔离仓(Q_E)的SEIR传染病动力学模型，旨在从动力学角度量化评估潜伏期隔离措施对传染病传播的影响。利用下一代矩阵法推导了模型的基本再生数R₀，作为判定传染病是否消亡的阈值；通过Lyapunov第二方法与LaSalle不变集原理，严格证明了当R₀ < 1时无病平衡点的全局渐近稳定性；利用灵敏度分析识别出影响传染病传播的关键参数。数值模拟结果表明，提高疫苗接种率及潜伏者隔离率能显著降低感染峰值、延缓传染病传播进程、缩短传染病持续时间。该研究针对潜伏期实施精准隔离、协同推进疫苗接种的防控策略提供了理论依据与决策支持。

Abstract: This paper constructs a class of SEIR infectious disease dynamics models that incorporate a quarantine compartment for latent individuals, aiming to quantitatively assess the impact of latent-period isolation measures on disease transmission from a dynamical perspective. Using the next-generation matrix method, the basic reproduction number (R₀) is derived as the threshold for determining whether the infectious disease will die out. Through Lyapunov second method and LaSalle invariance principle, the global asymptotic stability of the disease-free equilibrium is rigorously proved. Sensitivity analysis is applied to identify key parameters influencing disease transmission. Numerical simulation results demonstrate that increasing the vaccination rate and the isolation rate of latent individuals can significantly reduce the peak number of infections, delay the spread process, and shorten the duration of the epidemic. This study provides theoretical foundations and decision-making support for the precise implementation of isolation during the latent period and the coordinated promotion of vaccination as part of prevention and control strategies.