L-268 The Application of Herd Immunity to Munitions Safety

This report addresses the implications of the presence of both conventional and insensitive munitions (IM) in a national stockpile, and presents theoretical methods to determine a critical amount or fraction of IM that may avoid escalation of accident scenarios (e.g. mass detonation). An analogy can be made to herd immunity, which helps restrain the spread of contagious disease within a population if a sufficiently high proportion of individuals are immune to the disease, especially through vaccination. The analogy can be extrapolated by assuming that an IM-round will not sympathetically react (i.e. become infected) when next to an exploding non-IM-round (i.e. the contagion). Further, if enough IM-rounds are inserted into a distribution of munitions, there should be a statistical benefit and reduction of reaction violence that is greater than the effect of simply the inserted IM-rounds.  

Two new mathematical approaches have been introduced to determine the effective reproduction number (Re) and herd immunity threshold (HIT) in munitions safety problems. The first approach describes the propagation of detonation in a 2D random distribution of munitions. A second approach considers munition responses in more detail in a 1D configuration. This theoretical basis may help national authorities assess the interim benefits of IM investments, during the period when inventories are only partially converted.  Further, the report helps form a framework to more accurately estimate the safety benefits for military personnel, infrastructure, and equipment. The results of this study can be used to inform mixing rules and risk assessments.