Outbreak minimization v.s. influence maximization: an optimization framework.

Background: 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. 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.

Methods: We 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.

Results: A 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.

Conclusions: We 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.