COVID-19 has posed unprecedented challenges to medical tourism due to the global nature of its pandemic effect. Government support plays an essential role in the recovery and further development of the medical tourism industry. With the support of government, medical tourism enterprises, on the one hand, will maintain their daily business operations and wait for the mitigation of the pandemic. On the other hand, they will carry out information technology innovation in medical tourism and develop new businesses to create profits. Therefore, we construct a multitask principal-agent model for government and enterprises in the medical tourism industry, and discuss the influence of several critical exogenous variables on the decision strategies of the government and enterprises from the perspective of resilience. Numerical simulation is used to verify the effectiveness of the relevant conclusions. This paper can provide some decision-making basis and reference to realize the digital transformation and sustainable development of medical tourism industry under the COVID-19 crisis.