An epidemic model with the closed management in Chinese universities for COVID-19 prevention

Abstract

Abstract COVID-19 has deeply changed people’s way of life. While the anti-epidemic work in Chine has been successful, many Chinese universities still prohibit students from leaving the campus. In the meanwhile, faculty and staff can be on or off campus at will. This paper establishes an SI model to describe such a phenomenon. It is assumed that the latent population in society is a tiny constant, to which only a fraction of university population is exposed. Due to the closed management, a single individual cannot be exposed to the university and social population at the same time. A set of differential equations are proposed, and the standard solution is found. The results show that the entire closeness makes the virus not transmit in the university, and partial closeness leads the virus to spread on campus. By numerical simulation, the latent proportion as a function of different off-campus-allowed proportions is presented. It is found that to minimize the latent proportion, as many individuals should be allowed to be off-campus as possible when they are less likely to leave the campus, and there exists optimum allowed proportion when they are more likely to leave the campus. Furthermore, based on theoretical analysis, a quantitative formula describing the optimum allowed proportion in the general situations is given, providing the university administration with a method to calculate the optimum policy.