We create a network model to study the spread of an epidemic through physically proximate and accidental daily human contacts in a city, and simulate outcomes for two kinds of agents-poor and non-poor. Under non-intervention, peak caseload is maximised, but no differences are observed in infection rates across poor and non-poor. Introducing interventions to control spread, peak caseloads are reduced, but both cumulative infection rates and current infection rates are systematically higher for the poor than for non-poor, across all scenarios. Larger populations, higher fractions of poor, and longer durations of intervention are found to progressively worsen outcomes for the poor; and these are of particular concern for economically vulnerable populations in cities of the developing world. Addressing these challenges requires a deeper, more rigorous understanding of the relationships between structural poverty and epidemy, as well as effective utilization of extant community level infrastructure for primary care in developing cities. Finally, improving iniquitous outcomes for the poor creates better outcomes for the whole population, including the non-poor.