Analyze the Optimal International Allocation of Vaccine to Maximize Benefit in Terms of Minimizing the Risk of Infection

The COVID-19 pandemic brought the problem of disparities in vaccine production and distribution among nations into sharp focus, as this problem may leave people in low-income countries more vulnerable to the virus. Based on this background, this paper introduces a model that helps donors determine their vaccine donation strategy, aiming to maximize donor benefit by minimizing the risk of infection for their domestic people. Meanwhile, by receiving donated vaccines, the lower-income countries would also benefit, leading to a win-win situation. This model is based on a simplified condition where there are only two countries, and each vaccine is used by domestic people or donated to the other country. By analyzing the effects of the risk of disease, the relative importance of vaccines, and the level of contact between countries, this essay provides an equation that enables the calculation of the optimal number of vaccines that should be consumed by domestic people given the values of parameters. It analyzes the relationship between each parameter and the optimal number. This simple model can be employed to inspire the allocation of resources for other infectious diseases or similar situations.