Hand, foot and mouth (HFM) disease is a common childhood illness. The paper aims to capture the spatiotemporal characters, and investigate the influence factors of the HFM epidemic in 15 regions of Xinjiang province from 2008 to 2017, China. Descriptive statistical analysis shows that the children aged 0-5 years have a higher HFM incidence, mostly boys. The male-female ratio is 1.5:1. Through the scanning method, we obtain the first cluster high-risk areas. The cluster time is usually from May to August every year. A spatiotemporal model is proposed to analyze the impact of meteorological factors on HFM disease. Comparing with the spatial model, the model is more effective in terms of R2, AIC, deviation, and mean-square error. Among meteorological factors, the number of HFM cases generally increases with the intensity of rainfall. As the temperature increases, there are more HFM patients. Some regions are mostly influenced by wind speed. Further, another spatiotemporal model is introduced to investigate the relationship between HFM disease and socioeconomic factors. The results show that socioeconomic factors have significant influence on the disease. In most areas, the risk of HFM disease tends to rise with the increase of the gross domestic product, the ratios of urban population and tertiary industry. The incidence is closely related to the number of beds and population density in some regions. The higher the ratio of primary school, the lower the number of HFM cases. Based on the above analysis, it is the key measure to prevent and control the spread of the HFM epidemic in high-risk areas, and influence factors should not be ignored.

Sub-Saharan Africa has been the epicenter of the outbreak since the spread of acquired immunodeficiency syndrome (AIDS) began to be prevalent. This article proposes several regression models to investigate the relationships between the HIV/AIDS epidemic and socioeconomic factors (the gross domestic product per capita, and population density) in ten countries of Sub-Saharan Africa, for 2011–2016. The maximum likelihood method was used to estimate the unknown parameters of these models along with the Newton–Raphson procedure and Fisher scoring algorithm. Comparing these regression models, there exist significant spatiotemporal non-stationarity and auto-correlations between the HIV/AIDS epidemic and two socioeconomic factors. Based on the empirical results, we suggest that the geographically and temporally weighted Poisson autoregressive (GTWPAR) model is more suitable than other models, and has the better fitting results.

In medical studies, the binary data is often encountered when the paired organs or body parts receive treatment. However, the same treatment may lead to different therapeutic effects based on the stratified factors or confounding effects. Under Dallal’s model, the paper proposes the homogeneity test of risk difference to determine the necessity of stratified treatment. When the stratification is not necessary, common test is introduced to investigate if the risk difference is equal to a fixed constant between two groups. Several statistical tests are derived to analyze homogeneity and common hypotheses, respectively. Monte Carlo simulations show that the score tests behave well in both of hypotheses. Wald-type and Rosner’s statistics are always liberal but have higher empirical powers. Especially, the likelihood ratio statistic is better for the homogeneity test in the case of smaller data with larger strata. Two real examples are provided to illustrate the effectiveness of the proposed methods in ankle instability and otolaryngology studies.

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This paper proposes three methods to estimate the parameters in uncertain differential equations (UDEs) based on discrete observation data. The first method is designed for a class of UDEs in which their solutions have the explicit expressions of uncertainty distribution. The second method is given to solve the estimation problem through the inverse uncertainty distribution. In the third method, the unknown parameters of UDEs are estimated by the solution of the corresponding α-path. These methods are interpreted to be efficient and practical by using a popular UDE with exponential solutions and obtaining the detailed estimators of the parameters.