Emerging Infections and Nested Martingales: The Entrainment of Affluent Populations into the Disease Ecology of Marginalization

The observed diffusion of tuberculosis and AIDS from marginalized, inner-city populations to surrounding suburban counties, and of AIDS from larger to smaller metropolitan regions, constitutes an empirical ‘failure of containment’ at odds with the culturally defined ideology of the US system of de facto apartheid. Such spread, occurring along the commuting field defined by the daily journey to work, and along national travel routes connecting metropolitan regions, is characterized, respectively, as ‘spatially contagious' and as ‘hierarchical’ by geographers. Here we explore the nested ecology of these and similar infections by using the martingale theorem of probability theory to study the endemic limit and apply Ito's stochastic calculus to analyze the approach to endemicity. We find that increasing segregation and marginalization of subpopulations creates, in terms of incurable infectious disease, the paradox of a highly integrated apartheid system, entraining the rich into the diseases of the poor across vast scales of space and population, in effect poisoning the public health well for all. We suggest that, on the global scale, analogous processes can entrain the affluent North into the suffering of the South, particularly through the importation and redistribution of emerging infections.