HIV is one of the major life-threatening viruses that are spreading in the People’s Republic of China (China for short). A susceptible-exposed in the latent stage-infectious (SEI) model is established to sketch the evolution of epidemic. The basic reproduction number is defined. By constructing Lyapunov function, globally asymptotical stabilities of the disease-free and endemic equilibria are given. Then, optimal control theory is applied in HIV/AIDS epidemic. Precaution, screening, and treatment of control variables are introduced and a new model with control is established. Through the HIV/AIDS data in China, all parameters involved in SEI model are analyzed and parts of them are estimated. Further, by control model, optimal strategy is obtained. Results show that the precaution and treatment are the major contributors to preventing and controlling HIV/AIDS epidemic.

This paper extends the classical susceptible-infected-susceptible (SIS) epidemic model from a deterministic framework to an uncertain one and formulates it as an uncertain differential equation (UDE) for SIS epidemic model. The solutions of UDE SIS model and the corresponding α-paths are obtained. Under some conditions, these α-paths have the convergence properties. Further, a general uncertain SIS model is introduced. It’s solutions and α-paths are given. An algorithm is provided to solve α-paths and uncertain distributions of the UDE SIS model, including some examples.

In this article, we investigate a class of stochastic SIRS-type epidemic models with nonlinear incidence. The threshold value is identified. The existence of the unique global positive solution with any positive initial value is established. The sufficient conditions for the extinction of the disease and the permanence in the mean of the model with probability one are also established. That is, if , then the disease is extinct with probability one under certain parametric restrictions, and if , then the model is permanent in the mean with probability one. Furthermore, when there is not the disease-related death, if , then the existence of unique stationary distribution of the model is obtained.

Hand, foot, and mouth disease (HFMD) is a common childhood infectious disease. The incidence of HFMD has a pronounced seasonal tendency and is closely related to meteorological factors such as temperature, rainfall, and wind speed. In this paper, we propose a combined SARIMA-XGBoost model to improve the prediction accuracy of HFMD in 15 regions of Xinjiang, China. The SARIMA model is used for seasonal trends, and the XGBoost algorithm is applied for the nonlinear effects of meteorological factors. The geographical and temporal weighted regression model is designed to analyze the influence of meteorological factors from temporal and spatial perspectives. The analysis results show that the HFMD exhibits seasonal characteristics, peaking from May to August each year, and the HFMD incidence has significant spatial heterogeneity. The meteorological factors affecting the spread of HFMD vary among regions. Temperature and daylight significantly impact the transmission of the disease in most areas. Based on the verification experiment of forecasting, the proposed SARIMA-XGBoost model is superior to other models in accuracy, especially in regions with a high incidence of HFMD.

This paper proposes asymptotic and exact methods for testing the equality of correlations for multiple bilateral data under Dallal’s model. Three asymptotic test statistics are derived for large samples. Since they are not applicable to small data, several conditional and unconditional exact methods are proposed based on these three statistics. Numerical studies are conducted to compare all these methods with regard to type I error rates (TIEs) and powers. The results show that the asymptotic score test is the most robust, and two exact tests have satisfactory TIEs and powers. Some real examples are provided to illustrate the effectiveness of these tests.