Modelling the Containment of Viruses with Self-Disseminating Vaccines on Graphs

Abstract

An increasingly prominent topic in the field of immunology is the objective of limiting the spread of contagion in various animal populations. One recently presented solution is the use of self-disseminating vaccines. Self-disseminating vaccines are vaccines that are administered to small proportions of a large population of a species, with the property that the vaccine spreads itself autonomously. The theory behind their use is that at-risk populations could be identified, and then quickly inoculated with the use of a sparse number of optimally-distributed vaccines. We study the most efficient distributions of these vaccines on graphs, creating a model designed to determine optimal strategies for their use. In particular, we determine the minimum number of self-disseminating vaccines that must be used to contain the spread of a virus or contagion on several infinite graphs, as well as the best way to use a single selfdisseminating vaccine to preserve as much of a population from infection as possible on several finite graphs