This paper introduces the SIRS contagion model of food safety risk considering the entry rate, the normal bankruptcy rate, the abnormal bankruptcy rate, and other correlated parameters of food enterprise. The influences of these correlated factors on the contagion of food safety risk is discussed and theoretically analyzed. Computer simulation was performed to measure the entry rate of food enterprises, the normal bankruptcy rate, the abnormal bankruptcy rate, the re‐violation rate, the recovery rate, and the connectivity of food enterprises. The study found that: (a) the inhibitory effect of the normal bankruptcy rate on food safety risk contagion is the most significant; (b) the abnormal bankruptcy rate and the recovery rate can also constrain food safety risk, but the re‐violation rate will scale up the food safety risk; (c) a negative correlation exists between the entry rate and the contagion threshold of food safety risk, and a positive correlation is observed between the entry rate and the contagion scale of food safety risk; (d) with the increasing number of food enterprises' business partners, the contagion scale of food safety risk will increase. Practical applications This study is significant in supervising and managing the food market because it analyzes the contagion mechanism and the influence factors of food safety risk in the food supply network. According to the research results, we could take corresponding effective actions which introduced in the research to control the contagion scale of food safety risk and to guard the safety of food market.

In the growing market of health food, certain disturbances occur, such as uneven quality of products, imitation of health food, prohibited drug content in health food, functional efficacy, and actual disagreement. The safety of health food has attracted wide attention from all walks of life. In this study, we constructed a three-party game model of health food safety risk evolution, which includes health food enterprises, health food consumers, and government regulators, based on prospect theory and evolutionary game method. We also consider the attributes of “trust products” of health food, the ability to identify the safety information of health food, the subjective perception of the efficacy of health food, and the certification effect of the regulatory information of the government supervision department. The influence mechanism of these factors, including the cost of searching for health food information, consumers' subjective perception of health food efficiency, and the certification effect of supervision departments, on health food safety risk evolution is described using theoretical deduction and simulation analysis. On this basis, the corresponding conclusions are established, which provide a theoretical basis for further exploration of the strategy of health food market governance.