Global warming caused by carbon emissions has become increasingly prominent. As the world’s second-largest economy, China is under enormous pressure to cut down its carbon dioxide emissions. It is urgent to seek effective methods to forecast carbon emissions and put forward the pointed and effective measures to reduce emissions. In this paper, we first use the software Eviews to make an analysis of randomness on data of carbon emissions in the four representative provinces and city, Beijing, Henan, Guangdong, and Zhejiang, in terms of their carbon emissions data from 1997 to 2017. Then, according to their distinct characteristics, the methods of stationary processing of the difference, moving average, and substituting strong impact points, respectively, are adopted to perform the data preprocessing. Then, model identification, parameter estimation, and model test are carried out to establish the model of ARIMA(, d, q) for the prediction of the carbon emissions of the four regions, respectively. Finally, the model is used to forecast the data and analyze their tendency for their carbon emissions in the next three years. The results can provide guidance for decision-makers to set reasonable carbon emission reduction targets and take appropriate energy conservation and emission reduction measures.

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.

As COVID‐19 in some countries has increasingly become more severe, there have been significant efforts to develop models that forecast its evolution there. These models can help to control and prevent the outbreak of these infections. In this paper, we make long‐term predictions based on the number of current confirmed cases, accumulative recovered cases, and dead cases of COVID‐19 in some countries by the modeling approach. We use the SIRD (S: susceptible, I: infected, R: recovered, D: dead) epidemic model which is a nonautonomous dynamic system with incubation time delay to study the evolution of COVID‐19 in some countries. From the analysis of the recent data, we find that the cure and death rates may not be constant and, in some countries, they are piecewise functions. They can be estimated from the delayed SIRD model by the finite difference method. According to the recent data and its subsequent cure and death rates, we can accurately estimate the parameters of the model and then predict the evolution of COVID‐19 there. Through the predicted results, we can obtain the turning points, the plateau period, and the maximum number of COVID‐19 cases. The predicted results suggest that the epidemic situation in some countries is very serious. It is advisable for the governments of these countries to take more stringent and scientific containment measures. Finally, we studied the impact of the infection rate β on COVID‐19. We find that when the infection rate β decreases, the cumulative number of confirmed cases and the maximum number of currently infected cases will greatly decrease. The results further affirm that the containment techniques taken by these countries to curb the spread of COVID‐19 should be strengthened further.