在本文中,我们根据当前确诊病例的数量进行长期预测,通过建模方法研究中国不同地区COVID-19的累计死亡病例。首先,我们使用SIRD流行病模型(S-Susceptible,我感染了,R-恢复,D-Dead)是一个具有孵化时间延迟的非自治动态系统,用于研究武汉市COVID-19的演变,湖北省和中国大陆。根据前期中国国家卫生健康委员会发布的数据,我们可以准确地估计模型的参数,然后准确预测那里的COVID-19的演变。从发布的数据分析来看,我们发现武汉市的治愈率,湖北省和中国大陆是时间t的近似线性递增函数,其死亡率是分段递减函数。这些可以通过有限差分法估计。其次,我们使用延迟SIRD流行模型来研究COVID-19在武汉市以外的湖北省的演变。我们发现其治愈率是近似线性增加的函数,其死亡率几乎是一个常数。第三,我们使用延迟SIR流行模型(S-Susceptible,我感染了,R-删除)来预测北京的情况,上海,浙江省和安徽省。我们发现它们的治愈率是近似线性增加的函数,它们的死亡率是小常数。结果表明,可以对当前确认的数量进行准确的长期预测,通过建模,COVID-19的累计死亡病例。本文的结果表明,我们可以准确地获得和预测转折点,中国目前感染和死亡病例的结束时间和最大数量。尽管我们的方法简单,数据小,它在COVID-19的长期预测中相当有效。
In this paper, we make long-term predictions based on numbers of current confirmed cases, accumulative dead cases of COVID-19 in different regions in China by modeling approach. Firstly, we use the SIRD epidemic model (S-Susceptible, I-Infected, R-Recovered, D-Dead) which is a non-autonomous dynamic system with incubation time delay to study the evolution of the COVID-19 in Wuhan City, Hubei Province and China Mainland. According to the data in the early stage issued by the National Health Commission of China, we can accurately estimate the parameters of the model, and then accurately predict the evolution of the COVID-19 there. From the analysis of the issued data, we find that the cure rates in Wuhan City, Hubei Province and China Mainland are the approximately linear increasing functions of time t and their death rates are the piecewisely decreasing functions. These can be estimated by finite difference method. Secondly, we use the delayed SIRD epidemic model to study the evolution of the COVID-19 in the Hubei Province outside Wuhan City. We find that its cure rate is an approximately linear increasing function and its death rate is nearly a constant. Thirdly, we use the delayed SIR epidemic model (S-Susceptible, I-Infected, R-Removed) to predict those of Beijing, Shanghai, Zhejiang and Anhui Provinces. We find that their cure rates are the approximately linear increasing functions and their death rates are the small constants. The results indicate that it is possible to make accurate long-term predictions for numbers of current confirmed, accumulative dead cases of COVID-19 by modeling. In this paper the results indicate we can accurately obtain and predict the turning points, the end time and the maximum numbers of the current infected and dead cases of the COVID-19 in China. In spite of our simple method and small data, it is rather effective in the long-term prediction of the COVID-19.