  The COVID-19 pandemic has shed light on how the spread of infectious diseases
worldwide are importantly shaped by both human mobility networks and
socio-economic factors. Few studies, however, have examined the interaction of
mobility networks with socio-spatial inequalities to understand the spread of
infection. We introduce a novel methodology, called the Infection Delay Model,
to calculate how the arrival time of an infection varies geographically,
considering both effective distance-based metrics and differences in regions'
capacity to isolate -- a feature associated with socioeconomic inequalities. To
illustrate an application of the Infection Delay Model, this paper integrates
household travel survey data with cell phone mobility data from the S\~ao Paulo
metropolitan region to assess the effectiveness of lockdowns to slow the spread
of COVID-19. Rather than operating under the assumption that the next pandemic
will begin in the same region as the last, the model estimates infection delays
under every possible outbreak scenario, allowing for generalizable insights
into the effectiveness of interventions to delay a region's first case. The
model sheds light on how the effectiveness of lockdowns to slow the spread of
disease is influenced by the interaction of mobility networks and
socio-economic levels. We find that a negative relationship emerges between
network centrality and the infection delay after lockdown, irrespective of
income. Furthermore, for regions across all income and centrality levels,
outbreaks starting in less central locations were more effectively slowed by a
lockdown. Using the Infection Delay Model, this paper identifies and quantifies
a new dimension of disease risk faced by those most central in a mobility
network.
