Analysis of a COVID-19 Epidemic Model with Seasonality.

The statistics of COVID-19 cases exhibits seasonal fluctuations in many countries. In this paper, we propose a COVID-19 epidemic model with seasonality and define the basic reproduction number [Formula: see text] for the disease transmission. It is proved that the disease-free equilibrium is globally asymptotically stable when [Formula: see text], while the disease is uniformly persistent and there exists at least one positive periodic solution when [Formula: see text]. Numerically, we observe that there is a globally asymptotically stable positive periodic solution in the case of [Formula: see text]. Further, we conduct a case study of the COVID-19 transmission in the USA by using statistical data.

Preliminary prediction of the control reproduction number of COVID-19 in Shaanxi Province, China.

OBJECTIVES: Firstly, according to the characteristics of COVID-19 epidemic and the control measures of the government of Shaanxi Province, a general population epidemic model is established. Then, the control reproduction number of general population epidemic model is obtained. Based on the epidemic model of general population, the epidemic model of general population and college population is further established, and the control reproduction number is also obtained. METHODS: For the established epidemic model, firstly, the expression of the control reproduction number is obtained by using the next generation matrix. Secondly, the real-time reported data of COVID-19 in Shaanxi Province is used to fit the epidemic model, and the parameters in the model are estimated by least square method and MCMC. Thirdly, the Latin hypercube sampling method and partial rank correlation coefficient (PRCC) are adopted to analyze the sensitivity of the model. CONCLUSIONS: The control reproduction number remained at 3 from January 23 to January 31, then gradually decreased from 3 to slightly greater than 0.2 by using the real-time reports on the number of COVID-19 infected cases from Health Committee of Shaanxi Province in China. In order to further control the spread of the epidemic, the following measures can be taken: (i) reducing infection by wearing masks, paying attention to personal hygiene and limiting travel; (ii) improving isolation of suspected patients and treatment of symptomatic individuals. In particular, the epidemic model of the college population and the general population is established, and the control reproduction number is given, which will provide theoretical basis for the prevention and control of the epidemic in the colleges.