A novel grey model based on traditional Richards model and its application in COVID-19

Analysis of COVID-19 outbreak in Hubei province based on Tencent's location big data

Rapid urbanization has gradually strengthened the spatial links between cities, which greatly aggravates the possibility of the spread of an epidemic. Traditional methods lack the early and accurate detection of epidemics. This study took the Hubei province as the study area and used Tencent's location big data to study the spread of COVID-19. Using ArcGIS as a platform, the urban relation intensity, urban centrality, overlay analysis, and correlation analysis were used to measure and analyze the population mobility data of 17 cities in Hubei province. The results showed that there was high similarity in the spatial distribution of urban relation intensity, urban centrality, and the number of infected people, all indicating the spatial distribution characteristics of "one large and two small" distributions with Wuhan as the core and Huanggang and Xiaogan as the two wings. The urban centrality of Wuhan was four times higher than that of Huanggang and Xiaogan, and the urban relation intensity of Wuhan with Huanggang and Xiaogan was also the second highest in the Hubei province. Meanwhile, in the analysis of the number of infected persons, it was found that the number of infected persons in Wuhan was approximately two times that of these two cities. Through correlation analysis of the urban relation intensity, urban centrality, and the number of infected people, it was found that there was an extremely significant positive correlation among the urban relation intensity, urban centrality, and the number of infected people, with an R² of 0.976 and 0.938, respectively. Based on Tencent's location big data, this study conducted the epidemic spread research for "epidemic spatial risk classification and prevention and control level selection" to make up for the shortcomings in epidemic risk analysis and judgment. This could provide a reference for city managers to effectively coordinate existing resources, formulate policy, and control the epidemic.

Two novel nonlinear multivariate grey models with kernel learning for small-sample time series prediction

For many applications, small-sample time series prediction based on grey forecasting models has become indispensable. Many algorithms have been developed recently to make them effective. Each of these methods has a specialized application depending on the properties of the time series that need to be inferred. In order to develop a generalized nonlinear multivariable grey model with higher compatibility and generalization performance, we realize the nonlinearization of traditional GM(1,N), and we call it NGM(1,N). The unidentified nonlinear function that maps the data into a better representational space is present in both the NGM(1,N) and its response function. The original optimization problem with linear equality constraints is established in terms of parameter estimation for the NGM(1,N), and two different approaches are taken to solve it. The former is the Lagrange multiplier method, which converts the optimization problem into a linear system to be solved; and the latter is the standard dualization method utilizing Lagrange multipliers, that uses a flexible estimation equation for the development coefficient. As the size of the training data increases, the estimation results of the potential development coefficient get richer and the final estimation results using the average value are more reliable. The kernel function expresses the dot product of two unidentified nonlinear functions during the solving process, greatly lowering the computational complexity of nonlinear functions. Three numerical examples show that the LDNGM(1,N) outperforms the other multivariate grey models compared in terms of generalization performance. The duality theory and framework with kernel learning are instructive for further research around multivariate grey models to follow.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11071-023-08296-y.

Application of logistic differential equation models for early warning of infectious diseases in Jilin Province

Background

There is still a relatively serious disease burden of infectious diseases and the warning time for different infectious diseases before implementation of interventions is important. The logistic differential equation models can be used for predicting early warning of infectious diseases. The aim of this study is to compare the disease fitting effects of the logistic differential equation (LDE) model and the generalized logistic differential equation (GLDE) model for the first time using data on multiple infectious diseases in Jilin Province and to calculate the early warning signals for different types of infectious diseases using these two models in Jilin Province to solve the disease early warning schedule for Jilin Province throughout the year.

Methods

Collecting the incidence of 22 infectious diseases in Jilin Province, China. The LDE and GLDE models were used to calculate the recommended warning week (RWW), the epidemic acceleration week (EAW) and warning removed week (WRW) for acute infectious diseases with seasonality, respectively.

Results

Five diseases were selected for analysis based on screening principles: hemorrhagic fever with renal syndrome (HFRS), shigellosis, mumps, Hand, foot and mouth disease (HFMD), and scarlet fever. The GLDE model fitted the above diseases better (0.80 ≤ R2 ≤ 0.94, P <  0. 005) than the LDE model. The estimated warning durations (per year) of the LDE model for the above diseases were: weeks 12–23 and 40–50; weeks 20–36; weeks 15–24 and 43–52; weeks 26–34; and weeks 16–25 and 41–50. While the durations of early warning (per year) estimated by the GLDE model were: weeks 7–24 and 36–51; weeks 13–37; weeks 11–26 and 39–54; weeks 23–35; and weeks 12–26 and 40–50.

Conclusions

Compared to the LDE model, the GLDE model provides a better fit to the actual disease incidence data. The RWW appeared to be earlier when estimated with the GLDE model than the LDE model. In addition, the WRW estimated with the GLDE model were more lagged and had a longer warning time.

Predicting the Number of Reported Pulmonary Tuberculosis in Guiyang, China, Based on Time Series Analysis Techniques

Tuberculosis (TB) is one of the world's deadliest infectious disease killers today, and despite China's increasing efforts to prevent and control TB, the TB epidemic is still very serious. In the context of the COVID-19 pandemic, if reliable forecasts of TB epidemic trends can be made, they can help policymakers with early warning and contribute to the prevention and control of TB. In this study, we collected monthly reports of pulmonary tuberculosis (PTB) in Guiyang, China, from January 1, 2010 to December 31, 2020, and monthly meteorological data for the same period, and used LASSO regression to screen four meteorological factors that had an influence on the monthly reports of PTB in Guiyang, including sunshine hours, relative humidity, average atmospheric pressure, and annual highest temperature, of which relative humidity (6-month lag) and average atmospheric pressure (7-month lag) have a lagging effect with the number of TB reports in Guiyang. Based on these data, we constructed ARIMA, Holt-Winters (additive and multiplicative), ARIMAX (with meteorological factors), LSTM, and multivariable LSTM (with meteorological factors). We found that the addition of meteorological factors significantly improved the performance of the time series prediction model, which, after comprehensive consideration, included the ARIMAX (1,1,1) (0,1,2)₁₂ model with a lag of 7 months at the average atmospheric pressure, outperforms the other models in terms of both fit (RMSE = 37.570, MAPE = 10.164%, MAE = 28.511) and forecast sensitivity (RMSE = 20.724, MAPE = 6.901%, MAE = 17.306), so the ARIMAX (1,1,1) (0,1,2)₁₂ model with a lag of 7 months can be used as a predictor tool for predicting the number of monthly reports of PTB in Guiyang, China.

A novel grey model based on Susceptible Infected Recovered Model: A case study of COVD-19

The COVID-19 pandemic has lasted for nearly two years, and the global epidemic situation is still grim and growing. Therefore, it is necessary to make correct predictions about the epidemic to implement appropriate and effective epidemic prevention measures. This paper analyzes the classic Susceptible Infected Recovered Model (SIR) to understand the significance of model characteristics and parameters, and uses the differential and difference information of the grey system to put forward a grey prediction model based on SIR infectious disease model. The Laplace transform is used to calculate the model reduction formula, and finally obtain the modeling steps of the model. It is applied to large and small numerical cases to verify the validity of different orders of magnitude data. Meanwhile, data of different lengths are modeled and predicted to verify the robustness of model. Finally, the new model is compared with three classical grey prediction models. The results show that the model is significantly superior to the comparison model, indicating that the model can effectively predict the COVID-19 epidemic, and is applicable to countries with different population magnitude, can carry out stable and effective simulation and prediction for data of different lengths.

Forecasting the transmission trends of respiratory infectious diseases with an exposure-risk-based model at the microscopic level

Respiratory infectious diseases (e.g., COVID-19) have brought huge damages to human society, and the accurate prediction of their transmission trends is essential for both the health system and policymakers. Most related studies focus on epidemic trend forecasting at the macroscopic level, which ignores the microscopic social interactions among individuals. Meanwhile, current microscopic models are still not able to sufficiently decipher the individual-based spreading process and lack valid quantitative tests. To tackle these problems, we propose an exposure-risk-based model at the microscopic level, including 4 modules: individual movement, virion-laden droplet movement, individual exposure risk estimation, and prediction of transmission trends. Firstly, the front two modules reproduce the movements of individuals and the droplets of infectors' expiratory activities, respectively. Then, the outputs are fed to the third module to estimate the personal exposure risk. Finally, the number of new cases is predicted in the final module. By predicting the new COVID- 19 cases in the United States, the performances of our model and 4 other existing macroscopic or microscopic models are compared. Specifically, the mean absolute error, root mean square error, and mean absolute percentage error provided by the proposed model are respectively 2454.70, 3170.51, and 3.38% smaller than the minimum results of comparison models. The quantitative results reveal that our model can accurately predict the transmission trends from a microscopic perspective, and it can benefit the further investigation of many microscopic disease transmission factors (e.g., non-walkable areas and facility layouts).

Prediction intervals of the COVID-19 cases by HAR models with growth rates and vaccination rates in top eight affected countries: Bootstrap improvement

This paper is devoted to modeling and predicting COVID-19 confirmed cases through a multiple linear regression. Especially, prediction intervals of the COVID-19 cases are extensively studied. Due to long-memory feature of the COVID-19 data, a heterogeneous autoregression (HAR) is adopted with Growth rates and Vaccination rates; it is called HAR-G-V model. Top eight affected countries are taken with their daily confirmed cases and vaccination rates. Model criteria results such as root mean square error (RMSE), mean absolute error (MAE), R 2 , AIC and BIC are reported in the HAR models with/without the two rates. The HAR-G-V model performs better than other HAR models. Out-of-sample forecasting by the HAR-G-V model is conducted. Forecast accuracy measures such as RMSE, MAE, mean absolute percentage error and root relative square error are computed. Furthermore, three types of prediction intervals are constructed by approximating residuals to normal and Laplace distributions, as well as by employing bootstrap procedure. Empirical coverage probability, average length and mean interval score are evaluated for the three prediction intervals. This work contributes three folds: a novel trial to combine both growth rates and vaccination rates in modeling COVID-19; construction and comparison of three types of prediction intervals; and an attempt to improve coverage probability and mean interval score of prediction intervals via bootstrap technique.

Comparison of various epidemic models on the COVID-19 outbreak in Indonesia

This paper compares four mathematical models to describe Indonesia's current coronavirus disease 2019 (COVID-19) pandemic. The daily confirmed case data are used to develop the four models: Logistic, Richards, SIR, and SEIR. A least-square fitting computes each parameter to the available confirmed cases data. We conducted parameterization and sensitivity experiments by varying the length of the data from 60 until 300 days of transmission. All models are susceptible to the epidemic data. Though the correlations between the models and the data are pretty good (>90%), all models still show a poor performance (RMSE>18%). In this study case, Richards model is superior to other models from the highest projection of the positive cases of COVID-19 in Indonesia. At the same time, others underestimate the outbreak and estimate too early decreasing phase. Richards model predicts that the pandemic remains high for a long time, while others project the pandemic will finish much earlier.

Modeling and forecasting the COVID-19 pandemic with heterogeneous autoregression approaches: South Korea

This paper deals with time series analysis for COVID-19 in South Korea. We adopt heterogeneous autoregressive (HAR) time series models and discuss the statistical inference for various COVID-19 data. Seven data sets such as cumulative confirmed (CC) case, cumulative recovered (CR) case and cumulative death (CD) case as well as recovery rate, fatality rate and infection rates for 14 and 21 days are handled for the statistical analysis. In the HAR models, model selections of orders are conducted by evaluating root mean square error (RMSE) and mean absolute error (MAE) as well as R 2 , AIC, and BIC. As a result of estimation, we provide coefficients estimates, standard errors and 95% confidence intervals in the HAR models. Our results report that fitted values via the HAR models are not only well-matched with the real cumulative cases but also differenced values from the fitted HAR models are well-matched with real daily cases. Additionally, because the CC and the CD cases are strongly correlated, we use a bivariate HAR model for the two data sets. Out-of-sample forecastings are carried out with the COVID-19 data sets to obtain multi-step ahead predicted values and 95% prediction intervals. As for the forecasting performances, four accuracy measures such as RMSE, MAE, mean absolute percentage error (MAPE) and root relative square error (RRSE) are evaluated. Contributions of this work are three folds: First, it is shown that the HAR models fit well to cumulative numbers of the COVID-19 data along with good criterion results. Second, a variety of analysis are studied for the COVID-19 series: confirmed, recovered, death cases, as well as the related rates. Third, forecast accuracy measures are evaluated as small values of errors, and thus it is concluded that the HAR model provides a good prediction model for the COVID-19.

A new grey quadratic polynomial model and its application in the COVID-19 in China

This paper develops a new grey prediction model with quadratic polynomial term. Analytical expressions of the time response function and the restored values of the new model are derived by using grey model technique and mathematical tools. With observations of the confirmed cases, the death cases and the recovered cases from COVID-19 in China at the early stage, the proposed forecasting model is developed. The computational results demonstrate that the new model has higher precision than the other existing prediction models, which show the grey model has high accuracy in the forecasting of COVID-19.