带有干扰和非线性指标的脉冲时滞SI模型的渐近性质(英文)

The Asymptotic Property of an Impulsive Delay SI Model with Disturbance and a Nonlinear Incidence

研究了一个带有干扰和非线性指标的脉冲时滞SI模型,通过引入三个引理,获得该疾病最终灭绝和保持持久的充分性条件。结果表明,时滞因素对该模型的全局吸引性和持久性都有影响。此外。如果脉冲免疫接种率的最大值和最小值之比大于某一阈值,则该疾病最终灭绝,本文的主要特点是将多时滞和变系数引入脉冲SI模型,数值模拟表明,该系统具有复杂的动力学行为,包括周期解和周期振荡.

An impulsive delayed SI model with disturbance and a nonlinear incidence was formulated and analyzed.By introducing three thresholds,the sufficient conditions for eradication and permanence of the disease are obtained.Furthermore the global attractive of the infection-free periodic solution and permanence of the model are both influenced by time delay,the disease will disappear if the ratio of the maximum to minimum of the pulse vaccination rate is lager than some value.The main feature of this paper is that multi-delays and variable coefficients are introduced into the SI model.Numerical results show that the system has complex dynamics including the infection-free periodic solution and periodic oscillations.