Using Shannon Entropy to Improve the Identification of MP-SBM Models with Undesirable Output

In the context of the COVID-19 global epidemic, it is particularly important to use limited medical resources to improve the systemic control of infectious diseases. There is a situation where a shortage of medical resources and an uneven distribution of resources in China exist. Therefore, it is important to have an accurate understanding of the current status of the healthcare system in China and to improve the efficiency of their infectious disease control methods. In this study, the MP-SBM-Shannon entropy model (modified panel slacks-based measure Shannon entropy model) was proposed and applied to measure the disposal efficiency of the medical institutions responding to public health emergencies (disposal efficiency) in China from 2012 to 2018. First, a P-SBM (panel slacks-based measure) model, with undesirable outputs based on panel data, is given in this paper. This model measures the efficiency of all DMUs based on the same technical frontier and can be used for the dynamic efficiency analysis of panel data. Then, the MP-SBM model is applied to solve the specific efficiency paradox of the P-SBM model caused by the objective data structure. Finally, based on the MP-SBM model, undesirable outputs are considered in the original efficiency matrix alignment combination for the deficiencies of the existing Shannon entropy-DEA model. The comparative analysis shows that the MP-SBM-Shannon model not only solves the problem of the efficiency paradox of the P-SBM model but also improves the MP-SBM model identification ability and provides a complete ranking with certain advantages. The results of the study show that the disposal efficiency of the medical institutions responding to public health emergencies in China shows an upward trend, but the average combined efficiency is less than 0.47. Therefore, there is still much room for improvement in the efficiency of infectious disease prevention and control in China. It is found that the staffing problem within the Center for Disease Control and the health supervision office are two stumbling blocks.