We study allocation of COVID-19 vaccines to individuals based on the structural properties
of their underlying social contact network. Even optimistic estimates suggest that most
countries will likely take 6 to 24 months to vaccinate their citizens. These time estimates and
the emergence of new viral strains urge us to find quick and effective ways to allocate the vaccines
and contain the pandemic. While current approaches use combinations of age-based and occupation-based prioritizations, our strategy marks a departure from such largely aggregate vaccine allocation strategies. We propose a novel approach motivated by recent advances in (i) science of real-world networks that point to efficacy of certain vaccination strategies and (ii) digital technologies that improve our ability to estimate some of these structural properties. Using a realistic representation of a social contact network for the Commonwealth of Virginia, combined with accurate surveillance data on spatiotemporal cases and currently accepted models of within- and between-host disease dynamics, we study how a limited number of vaccine doses can be strategically distributed to individuals to reduce the overall burden of the pandemic. We show that allocation of vaccines based on individuals' degree (number of social contacts)
and total social proximity time is significantly more effective than the currently used age-based
allocation strategy in terms of number of infections, hospitalizations and deaths. Our results suggest that in just two months, by March 31, 2021, compared to age-based allocation, the
proposed degree-based strategy can result in reducing an additional 56−110k infections, 3.2−
5.4k hospitalizations, and 700−900 deaths just in the Commonwealth of Virginia. Extrapolating
these results for the entire US, this strategy can lead to 3−6 million fewer infections, 181−306k
fewer hospitalizations, and 51−62k fewer deaths compared to age-based allocation. The overall
strategy is robust even: (i) if the social contacts are not estimated correctly; (ii) if the vaccine efficacy is lower than expected or only a single dose is given; (iii) if there is a delay in vaccine production and deployment; and (iv) whether or not non-pharmaceutical interventions continue as vaccines are deployed. For reasons of implementability, we have used degree, which is a simple structural measure and can be easily estimated using several methods, including the digital technology available today. These results are significant, especially for resource-poor countries, where vaccines are less available, have lower efficacy, and are more slowly distributed.
Suppose that we are given two dominating sets Ds and Dt of a graph G whose cardinalities are at most a given threshold k. Then, we are asked whether there exists a sequence of dominating sets of G between Ds and Dt such that each dominating set in the sequence is of cardinality at most k and can be obtained from the previous one by either adding or deleting exactly one vertex. This problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this decision problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, trees, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence such that the number of additions and deletions is bounded by O(n), where n is the number of vertices in the input graph.
Motivated by the well known "four-thirds conjecture" for the traveling salesman problem (TSP), we study the problem of uniform covers. A graph G = (V, E) has an α-uniform cover for TSP (2EC, respectively) if the everywhere α vector (i.e. {α} E ) dominates a convex combination of incidence vectors of tours (2-edge-connected spanning multigraphs, respectively). The polyhedral analysis of Christofides' algorithm directly implies that a 3-edge-connected, cubic graph has a 1-uniform cover for TSP. Sebő asked if such graphs have (1 − )-uniform covers for TSP for some > 0 [SBS14]. Indeed, the four-thirds conjecture implies that such graphs have 8 9 -uniform covers. We show that these graphs have 18 19 -uniform covers for TSP. We also study uniform covers for 2EC and show that the everywhere 15 17 vector can be efficiently written as a convex combination of 2-edge-connected spanning multigraphs.For a weighted, 3-edge-connected, cubic graph, our results show that if the everywhere *
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.