Vaccine allocation scheme for regions with different epidemic spreading progressions

In this paper, the optimal vaccine allocation scheme when there are differences in the epidemic spreading progressions between different regions is studied. The results indicate that differences in spreading progressions, number of vaccines and control time all have a significant impact on the optimal vaccine allocation scheme, but the difference in spreading progressions has an essential effect: When the spreading progressions in two identical regions shift from being the same to having differences, the optimal vaccine allocation scheme also shifts from no preference to favoring the late spreading region. As the difference in spreading progressions increases, the optimal vaccine allocation scheme involves allocating an increasing number of vaccines to the late spreading region until a certain stable value is reached. However, as the total number of vaccines increases, the difference in the quantity of vaccines allocated to the two regions becomes smaller, and the difference almost disappears when there are enough vaccines to control both regions. Additionally, it is found that when the other conditions are the same, the later the control time, the more the vaccines should be allocated to the late spreading region. An in-depth analysis of the reasons behind these phenomena has been conducted and it’s found that the main reason is that at any given time, regions that started spreading late are actually at a relatively early stage of spreading progression, making them more easily controlled. Prioritizing the immunization of such regions will, overall, yield better control performance. Spreading experiments on real networks are also performed and the results confirm our conclusions. Our work provides theoretical guidance for allocating limited vaccines to regions with different epidemic spreading progressions.