Temporal-Spatial Evolution and Trend Prediction of the Supply Efficiency of Primary Medical Health Service—An Empirical Study Based on Central and Western Regions of China

China has established a comprehensive primary medical health service system, but the development of primary medical health services in the central and western regions is still unbalanced and insufficient. Based on data from 2010 to 2019, this paper constructs a super efficiency Slack-Based Measure model to calculate the supply efficiency of primary medical health services in 20 provinces and cities in central and western China. Using Kernel density estimation and Markov chain analysis, this paper further analyzes the spatial-temporal evolution of the supply efficiency of primary medical health services in central and western China, and also predicts the future development distribution through the limiting distribution of Markov chain to provide a theoretical basis for promoting the sinking of high-quality medical resources to the primary level. The results show that firstly, during the observation period, the center of the Kernel density curve moves to the left, and the main peak value decreases continuously. The main diagonal elements of the traditional Markov transition probability matrix are 0.7872, 0.5172, 0.8353, and 0.7368 respectively, which are significantly larger than other elements. Secondly, when adjacent to low state and high state, it will develop into convergence distributions of 0.7251 and 0.8243. The supply efficiency of primary medical health services in central and western China has the characteristics of high (Ningxia) and low (Shaanxi) aggregation respectively, but the aggregation trend is weakened. Thirdly, the supply efficiency of health services has the stability of keeping its own state unchanged, but the transition of state can still occur. The long-term development of the current trend cannot break the distribution characteristics of the high and low clusters, the efficiency will show a downward trend in the next 10–20 years, and still the problem of uneven long-term development emerges.