Research on the Spread of COVID-19 Based on the SEIR Model for Susceptible Populations With Basic Medical History
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摘要: 该文基于经典的SEIR传染病模型建立了一类含有基础疾病历史人群的新冠肺炎传播模型,得到了其传播的基本再生数,确定了模型平衡点的存在性,并通过构造Lyapunov函数和利用LaSalle不变性原理论证了平衡点的全局稳定性,用数值模拟对所得理论研究结果进行了有效验证.同时,讨论了由无基础病向有基础病转化的速率系数对疾病传播的影响,发现不考虑基础病的数学模型会低估疾病传播的基本再生数和感染规模,数值模拟也显示了由无基础病向有基础病转化的速率系数对感染者人数峰值的影响.Abstract: Based on the classic SEIR infectious disease model, a new type of new coronary pneumonia transmission model containing a population with a history of basic diseases was established, the basic reproduction number of its transmission was obtained, and the existence of the equilibrium of the model was determined. Through construction of the Lyapunov function and with the LaSalle invariance principle, the global stability of the equilibrium was proved, and the theoretical research results were also verified by numerical simulation. At the same time, the influence of the transformation rate coefficient from no basic medical disease to basic disease on the disease transmission was discussed. It is found that, the mathematical model considering no basic disease will underestimate the basic reproduction number of disease transmission and the scale of infection. Numerical simulations also show the definite impact of the transformation rate coefficient from no basic disease to basic disease on the peak number of the infected population.
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Key words:
- COVID-19 /
- basic disease /
- equilibrium /
- global asymptotic stability
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