Pulse vaccination is an effective strategy to restrain the spread of infectious diseases. This paper proposes a network-based SIR epidemic model incorporating a saturated force of infection and vertical transmission along with pulse vaccination strategy and continuous treatment plan. Dynamical behaviors of the model are analyzed in virtue of the theory for impulsive differential equations. We give the boundedness of solutions and derive the expression of basic reproduction number . By the Floquet theorem and comparison principle, we show that the disease-free periodic solution is globally asymptotically stable when . Moreover, a sufficient condition for the uniform permanence of the system is also obtained. Finally, numerical analyses are given to substantiate the theoretical results and a case for Rubella is studied.

中文翻译：

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具有饱和发病率和脉冲疫苗接种的基于网络的 SIR 流行病模型的动态行为


脉冲疫苗接种是抑制传染病传播的有效策略。本文提出了一种基于网络的 SIR 流行病模型，结合了饱和感染力和垂直传播以及脉冲疫苗接种策略和连续治疗计划。借助脉冲微分方程理论分析了模型的动力学行为。给出了解的有界性并推导了基本再生数的表达式。通过Floquet定理和比较原理，我们证明了当 时，无病周期解是全局渐近稳定的。此外，还获得了系统均匀持久的充分条件。最后，进行数值分析以证实理论结果，并研究了风疹的案例。