Government's Policy on Controlling the Covid-19 Virus Based on the Game Theory Approach: Closing Jobs or Purchasing Vaccines

The tools to control COVID-19 virus and this epidemic have been tested in all countries and at different levels. At the community level, they include observing hygienic principles, such as observing social distance, wearing masks, washing hands, observing cleanliness, observing personal belongings, and etc. Also at the macro level, governments have taken measures to combat the virus, such as closing cities, purchasing vaccines hygiene training. Given the high costs of closing cities and purchasing vaccines for governments, they may be willing to select and use a combination of them to control the virus. Considering these 2 factors as 2 competitors in the effectiveness of COVID-19 control, this study sought to find an equilibrium point to control the virus.

An infinite 2-player game was defined by considering the number of cities closed per person-day and the number of vaccine purchased per person, both of which have continuous and infinite space. On the other hand, a significant basic criterion for governments can be the cost and number of patients with the disease. Hence, the game was defined based on 2 criteria. A case study was also solved for the sake of clarity.

The government must close offices for at least 12 days and inject 2 doses of the vaccine to about 28 million people in order to achieve its goal of reducing costs and reducing the incidence of the disease.

By solving the proposed model, it was found that for the initial control of the disease, the purchase and injection of vaccines can be more effective, but in order to further reduce and control the disease, it is better to close jobs. Analyses also showed that governments that are less willing to spend money on disease control could close jobs.