In this paper, a discretized SIR model with pulse vaccination and time delay is proposed. We introduce two thresholds R* and R<sub>*</sub>, and further prove that the disease-free periodic solution is glob...In this paper, a discretized SIR model with pulse vaccination and time delay is proposed. We introduce two thresholds R* and R<sub>*</sub>, and further prove that the disease-free periodic solution is globally attractive if R* is less than unit and the disease can invade if R<sub>*</sub> is larger than unit. The numerical simulations not only illustrate the validity of our main results, but also exhibit bifurcation phenomenon. Our result shows that decreasing infection rate can put off the disease outbreak and reduce the number of infected individuals.展开更多
文摘In this paper, a discretized SIR model with pulse vaccination and time delay is proposed. We introduce two thresholds R* and R<sub>*</sub>, and further prove that the disease-free periodic solution is globally attractive if R* is less than unit and the disease can invade if R<sub>*</sub> is larger than unit. The numerical simulations not only illustrate the validity of our main results, but also exhibit bifurcation phenomenon. Our result shows that decreasing infection rate can put off the disease outbreak and reduce the number of infected individuals.
文摘截至2020-04-21,全球累计确诊新型冠状病毒肺炎(coronavirus disease 2019,COVID-19)病例数已超过245万人,死亡病例数超过17万人。根据疫情的发展过程,首先建立了改进的离散时间多阶段时滞动力学模型,以提取疫情的传播特征,解析防控干预的影响(防控干预效果)和医疗资源可用率的影响,并基于该模型,提出一种分析COVID-19的经验传递动力学方法。其中,经验提取是基于该模型与WHO(World Health Organization)发布的疫情数据,通过参数反演实现。然后利用该方法,分析了意大利、西班牙、德国和美国等国家疫情所处的阶段,预测不同措施下各国疫情的可能走向,给出了快速控制的建议。分析结果显示,中国疫情已基本得到控制,西班牙、德国、意大利已达到峰值,美国疫情正处于紧急防御期。依据经验传递动力学方法,建议西班牙、德国、意大利三国继续坚持目前的防控干预方式,美国加大防控力度,尽快使疫情进入可控阶段。
