Social disintegration and the spread of AIDS: thresholds for propagation along 'sociogeographic' networks

Previous work on the asymptotic spread of HIV infection along a low dimensional 'sociogeographic' network--a social network characteristically embedded within a limited geographic area--is extended to explore threshold conditions under which the infection extends widely beyond an initial set of infected individuals or communities. Results for one dimension suggest that threshold behavior is analogous to a chain reaction with criticality determined conjointly by the susceptibility of individuals within a community to a nexus of behavior conducive to rapid HIV spread and by the probability of transmission between susceptible communities. Once threshold is exceeded, a stochastic reformulation finds the asymptotic rate of transmission between communities may be markedly raised by positive correlation between susceptibility to rapid disease spread within a community and the transmissibility between communities, for example outmigration driven by social disintegration or residential instability arising from inherent structural factors associated with community susceptibility, as with male prostitution. Examination of threshold conditions for higher dimensional sociogeographic networks most likely characteristic of disease spread beyond the 'deep ghettos' now suffering the highest burden of infection suggests it is at least as, and likely more, effective to decrease the fraction of population susceptible to the high risk behavioral nexus as it is to lower the probability of disease transmission between susceptible individuals or communities.(ABSTRACT TRUNCATED AT 250 WORDS)