Abstract
BackgroundAn effective approach to containing epidemic outbreaks (e.g., COVID-19) is targeted immunization, which involves identifying “super spreaders” who play a key role in spreading disease over human contact networks. The ultimate goal of targeted immunization and other disease control strategies is to minimize the impact of outbreaks. It shares similarity with the famous influence maximization problem studied in the field of social network analysis, whose objective is to identify a group of influential individuals to maximize the influence spread over social networks. This study aims to establish the equivalence of the two problems and develop an effective methodology for targeted immunization through the use of influence maximization.MethodsWe present a concise formulation of the targeted immunization problem and show its equivalence to the influence maximization problem under the framework of the Linear Threshold diffusion model. Thus the influence maximization problem, as well as the targeted immunization problem, can be solved by an optimization approach. A Benders’ decomposition algorithm is developed to solve the optimization problem for effective solutions.ResultsA comprehensive computational study is conducted to evaluate the performance and scalability of the optimization approach on real-world large-scale networks. Computational results show that our proposed approaches achieve more effective solutions compared to existing methods.ConclusionsWe show the equivalence of the outbreak minimization and influence maximization problems and present a concise formulation for the influence maximization problem under the Linear Threshold diffusion model. A tradeoff between computational effectiveness and computational efficiency is illustrated. Our results suggest that the capability of determining the optimal group of individuals for immunization is particularly crucial for the containment of infectious disease outbreaks within a small network. Finally, our proposed methodology not only determines the optimal solutions for target immunization, but can also aid policymakers in determining the right level of immunization coverage.
Highlights
Introduction toBenders’ Decomposition The original mixed integer linear programming (MILP) formulation of the Time Aware Influence Maximization (TAIM) problem is difficult to solve, especially for large-scale instances
We first formulate Targeted immunization (TI) as an optimization problem and show that it is equivalent to the standard formulation of the influence maximization problem under the framework of the Linear Threshold (LT) diffusion model. e aim to answer the following research question: can we achieve more effective IT solutions by an optimization approach for the IM problem, as compared with existing methods? To be specific, our research achieves the following contributions: 1 We show that the TI problem is equivalent to the famous IM problem
To address the issue that existing IM methods are based on the greedy algorithm, which guarantees only (1 − 1/e) approximation on submodular diffusion functions, we present a novel and concise formulation of the IM problem on the LT model so that it can be solved by more effective optimization techniques
Summary
Introduction toBenders’ Decomposition The original MILP formulation of the TAIM problem is difficult to solve, especially for large-scale instances. An optimal solution for the original problem is obtained by combining the solutions of the master problem and subproblem from the last iteration. An effective approach to containing epidemic outbreaks (e.g., COVID-19) is targeted immunization, which involves identifying “super spreaders” who play a key role in spreading disease over human contact networks. The ultimate goal of targeted immunization and other disease control strategies is to minimize the impact of outbreaks. It shares similarity with the famous influence maximization problem studied in the field of social network analysis, whose objective is to identify a group of influential individuals to maximize the influence spread over social networks. The project aimed to investigate solutions for effective and timely responses to possible severe infectious disease outbreaks. While the individuals’ contact activities could be captured through this system, our question is: what is an effective way to containing the disease? This motivated our current research
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