This study investigates whether and how the two risk control strategies inhibit credit risk contagion among enterprises in the network. Learning from the corporate governance of enterprises, we propose internal and external strategies, respectively. Moreover, two improved epidemic models containing internal and external strategies strategy are established to investigate the impact of the two strategies on the risk contagion. The control effect of internal and external strategies is compared through simulation analysis. The results indicate that the enterprise's financial health, the cost and ability to apply the strategies are important factors affecting the control effect of strategies. For enterprises with general financial status (susceptible enterprise), when the costs of the two strategies are the same, they should choose external strategies. For enterprises with good financial status (immune enterprises), the external strategy is a more sensible choice. Our study provides new insights into controlling risk contagion in enterprise networks.