With the successful completion of the battle against poverty, after 2020, the focus and difficulty of China’s poverty governance will change from solving absolute poverty to alleviating relative poverty. Analyzing and studying the alleviation of relative poverty from the perspective of public health services is in line with the current needs of consolidating and expanding poverty alleviation in China, and it is also of great significance to building a long-term solution mechanism for relative poverty. In this study, basic panel data were constructed by using the data of five CFPS surveys in 2010, 2012, 2014, 2016, and 2018 and matched with the macro data. The correlation between public health services and rural households’ relative poverty was also analyzed by using logit regression analysis and the KHB mediation effect decomposition method. The results show that (1) public health services play a significant role in promoting the accumulation of health human capital, improving individual feasible ability, and alleviating the relative poverty of rural families; (2) the improvement of public health services is conducive to the alleviation of the relative poverty of rural families; (3) we should continue to increase investment in public health care in underdeveloped areas and strive to promote the balanced development of public health services, so as to further consolidate and expand the achievements of poverty eradication.

By introducing network game theory, this paper analyzes the internal relationship and interaction mechanism among environmental governance, local government competition, and agricultural carbon peak level. On the basis of theoretical analysis, a spatial panel model is constructed using panel data from 30 provincial-level regions in China for empirical analysis. The research finds that local governments have positive competition with respect to the agricultural carbon peak, they adopt complementary carbon peak competition strategies, and they are more inclined to take geographical distance to adjacent regions as the yardstick in the competition with respect to the agricultural carbon peak strategy. That is, when the carbon peak level of surrounding provinces increases, the carbon peak level of the region will also increase. Thus, there is a phenomenon of mutual imitation and convergence between neighboring provinces. Environmental governance has a significant positive direct effect and a positive spatial spillover effect. From the perspective of coefficient, its direct effect is significantly greater than the spatial spillover effect. Therefore, more attention should be paid to local environmental governance to promote the improvement of the agricultural carbon peak level. Furthermore, the agricultural industrial structure, fiscal decentralization, agricultural public investment, regional industrial structure, and the proportion of the rural population have significant spatial spillover effects. The agricultural industrial structure and fiscal decentralization are significantly positively correlated with the peak level of agricultural carbon while the proportion of the rural population is significantly negatively correlated with the peak level of agricultural carbon. The research results have important theoretical value for expanding the research in the field of agricultural carbon emissions and provide important practical reference for China to successfully achieve the goal of agricultural carbon peak and promote the high-quality development of agriculture