Abstract
In 2020, COVID-19 became a global pandemic. Older people are less resistant to the novel coronavirus. In order to ensure the health of the elderly population, the governments of five Central Asian countries should provide home medical services for the elderly or provide "green channel" to medical services. This "green channel" means providing a special service and treatment for the elderly in the hospital to ensure that they can safely and easily access the medical services they need. In order to study the application scope of various modes, this article constructs three modes of differential game: no special care, home medical care and "green channel". And the equilibrium results are compared and analyzed. Research shows that when the additional medical costs associated with house calls or "green channel" gradually increase, the social benefits to both the elderly and the government gradually decrease, and eventually it is less than the social benefits under the no-special care model. The greater the credibility of the government under the "green channel" service model, the greater the social benefits of the government. However, the greater the credibility of the government under the home medical service model, the smaller the social benefits of the government.