Mitigating an epidemic on a geographic network using vaccination
Mohamad Badaoui, Jean-Guy Caputo, Gustavo Cruz-Pacheco, Arnaud, Knippel

TL;DR
This paper develops a mathematical framework to optimize vaccination strategies on geographic networks by analyzing epidemic growth through eigenvalues, providing practical guidelines for epidemic control.
Contribution
It introduces a novel eigenvector-based vaccination strategy derived from matrix perturbation theory for epidemic mitigation on networks.
Findings
Vaccinating along the Laplacian eigenvector is most effective when mobility and disease dynamics are similar.
Targeting high-degree vertices reduces epidemic growth more effectively.
Slower mobility shifts focus to vertices with the largest susceptibles.
Abstract
We consider a mathematical model describing the propagation of an epidemic on a geographical network. The size of the outbreak is governed by the initial growth rate of the disease given by the maximal eigenvalue of the epidemic matrix formed by the susceptibles and the graph Laplacian representing the mobility. We use matrix perturbation theory to analyze the epidemic matrix and define a vaccination strategy, assuming the vaccination reduces the susceptibles. When mobility and local disease dynamics have similar time scales, it is most efficient to vaccinate the whole network because the disease grows uniformly. However, if only a few vertices can be vaccinated then which ones do we choose? We answer this question, and show that it is most efficient to vaccinate along an eigenvector corresponding to the largest eigenvalue of the Laplacian. We illustrate these general results on a 7…
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Taxonomy
TopicsComplex Network Analysis Techniques · Mathematical and Theoretical Epidemiology and Ecology Models · Opinion Dynamics and Social Influence
