We consider a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment. The treatment rate has at most a finite number of jump discontinuities in every compact interval. By using Lyapunov theory for discontinuous differential equations and other techniques on non-smooth analysis, the basic reproductive number R0 is proved to be a sharp threshold value which completely determines the dynamics of the model. If R0 ≤ 1, then there exists a disease-free equilibrium which is globally stable. If R0 > 1, the disease-free equilibrium becomes unstable and there exists an endemic equilibrium which is globally stable. We discuss that the disease will die out in a finite time which is impossible for the corresponding SEIR model with continuous treatment. Furthermore, the numerical simulations indicate that strengthening treatment measure after infective individuals reach some level is beneficial to disease control.

中文翻译：

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间断治疗策略下具有潜伏期和感染期感染力的SEIR流行病模型的全局稳定性

我们考虑在不连续治疗下具有潜伏期和感染期感染力的 SEIR 流行模型。处理率在每个紧凑区间中最多有有限数量的跳跃不连续性。利用李雅普诺夫理论对不连续微分方程等技术进行非光滑分析，得到基本再生数R0被证明是一个尖锐的阈值，它完全决定了模型的动态性。如果R0 ≤ 1，则存在全局稳定的无病平衡。如果R0 > 1，无病平衡变得不稳定，并且存在全局稳定的地方病平衡。我们讨论了这种疾病会在有限的时间内消失，这对于相应的 SEIR 模型进行连续治疗是不可能的。此外，数值模拟表明，在感染个体达到一定程度后加强治疗措施有利于疾病控制。