Global dynamics for an SVEIR epidemic model with diffusion and nonlinear incidence rate

In this paper, we investigate an SVEIR epidemic model with reaction-diffusion and nonlinear incidence. We establish the well-posedness of the solutions and the basic reproduction number R-0. Moreover, we show that the disease-free steady state is globally asymptotically stable when R-0 < 1, whereas the disease will be persistent when R-0 > 1. Furthermore, using the method of Lyapunov functional, we prove the global stability of the positive steady state for the spatial homogeneous model.

Research on Students' Course Selection Preference based on Collaborative Filtering Algorithm

Due to the events caused by the COVID-19 pandemic, the education industry is no longer limited to offline, and online classroom education is widely used. The rapid development of online education provides users with more abundant educational course resources and flexible learning methods. Various online education platforms are also constantly improving their service models to give users a better learning experience. However, at present, there are few personalized information recommendation services in student course selection. Students receive the same course selection information and cannot be "tailored" according to their specific preferences. This paper focuses on the integration of collaborative filtering technology into a college course selection system to construct a rating matrix based on students' ratings of the courses they take through correlation between courses and correlation between students. Based on the collaborative filtering algorithm, a predictive rating matrix is generated to produce a recommendation list to achieve intelligent recommendation of suitable courses for students. The experimental results show that, based on the traditional collaborative filtering recommendation technique, the improved collaborative filtering algorithm based on both item and user weighting is used to achieve course recommendation with higher recommendation accuracy. The application of the improved collaborative filtering technique in the course selection recommendation system of colleges and universities is very good at recommending courses for students intelligently, and the recommended courses for students have good rationality and accuracy, and achieve more intelligent course selection for students, which has great practicality and practical significance.