One long-standing question in epidemiological research is how best to allocate limited amounts of vaccine or similar preventative measures in order to minimize the severity of an epidemic. Much of the literature on the problem of vaccine allocation has focused on influenza epidemics and used mathematical models of epidemic spread to determine the effectiveness of proposed methods. Our work applies computational models of epidemics to the problem of geographically allocating a limited number of vaccines within several Texas counties. We developed a graph-based, stochastic model for epidemics that is based on the SEIR model, and tested vaccine allocation methods based on multiple centrality measures. This approach provides an alternative method for addressing the vaccine allocation problem, which can be combined with more conventional approaches to yield more effective epidemic suppression strategies. We found that allocation methods based on in-degree and inverse betweenness centralities tended to be the most effective at mitigating epidemics.
The p-median problem selects p source locations to serve n destinations such that the average distance between the destinations and corresponding sources is minimized. It is a well-studied NP-hard combinatorial optimization problem with many existing heuristic solutions, however, existing algorithms are not scalable for large-scale problems. The Fast Interchange (FI) heuristic which yields results close to the optimal solution with respect to the objective function value becomes suboptimal with respect to time requirements for large-scale problems. We present a novel distributed multi-core divide and conquer algorithm, EM-FI, to solve large-scale p-median problems quickly even with limited computing resources. The algorithm identifies the existing spatial clusters of the destination locations using Expectation Maximization(EM) and solves them as independent p-median problems using Integer Programming or FI concurrently. The proposed algorithm showed an order of magnitude improvement in time without the loss of quality in terms of the objective function value on synthetic and real datasets.
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