<p>The primary task in safeguarding health is preventing disease before it occurs, that is, reducing the incidence of disease through disease prevention and health management. To address the issues of disease prevention and difficulty in accessing medical care, this paper proposes introducing private home healthcare agencies to establish a public health co-governance system. By constructing a four-party evolutionary game model involving the healthcare system, home healthcare agencies, government departments, and the public, we can identify the factors influencing the strategy choices of each entity and determine stable strategy combinations. Research findings: 1) When the costs associated with actively supporting the “health+” hierarchical diagnosis and treatment are lower than those of substandard services compared to high-quality services, and the costs required for public acceptance are below the critical threshold, it is possible to ensure that the healthcare system, home healthcare agencies, and the public adopt beneficial strategies. 2) In some cases, government departments cannot effectively avoid the undesirable state from becoming a stable equilibrium no matter what supervision strategies they adopt, and it depends critically on the costs and benefits under different strategies of each party. 3) Active cooperation among the healthcare service system, home healthcare agencies and the public can reduce the probability of governmental supervision strategies, and governmental monitor is not necessary when the “health+” hierarchical diagnosis and treatment system works optimally. The study can provide a theoretical basis and reference for the government to improve family disease prevention capabilities and improve the hierarchical diagnosis and treatment system.</p>