Optimal vaccination strategies for COVID-19 in population migration between two regions scenario

Population movements had a significant impact on the spread of COVID-19, and vaccination is considered the most effective means for humans to face viral infections. This study identifies the optimal control strategy for COVID-19 prevention and control, and explores the impact of short-term and long-term migration on the optimal proportion of vaccine allocation between two regions. We proposed to establish the SIR (Susceptible-Infectious-Recovered) model and determine the stability by calculating the disease free equilibrium and Jacobi matrix of the model. We then established the vaccine optimization model, solved the optimal vaccine distribution strategy by gradient descent method and explored the impact of short-term and long-term migration on the optimal vaccine allocation ratio. The stability analysis revealed that the virus could not be eliminated only by reducing the migration rates and infection rates. we introduced the vaccine methods and obtained the optimal vaccine allocation ratio in Shenzhen and Hong Kong as $$, and the daily vaccination rate we need to impose in each region as $$. The presence or absence of short-term migration had no greater impact on the distribution of the vaccine, whereas $$ with long-term migration had a greater effect than no migration. We found that migration rates could not eliminate the outbreak in both regions and that adopting an effective vaccine distribution strategy could be more effective in eliminating the outbreak. And for different allocation scenarios with limited vaccine supply, we obtained the optimal allocation most favorable to control the epidemic.