  Understanding how people move within a geographic area, e.g. a city, a
country or the whole world, is fundamental in several applications, from
predicting the spatio-temporal evolution of an epidemics to inferring migration
patterns. Mobile phone records provide an excellent proxy of human mobility,
showing that movements exhibit a high level of memory. However, the precise
role of memory in widely adopted proxies of mobility, as mobile phone records,
is unknown. Here we use 560 millions of call detail records from Senegal to
show that standard Markovian approaches, including higher-order ones, fail in
capturing real mobility patterns and introduce spurious movements never
observed in reality. We introduce an adaptive memory-driven approach to
overcome such issues. At variance with Markovian models, it is able to
realistically model conditional waiting times, i.e. the probability to stay in
a specific area depending on individual's historical movements. Our results
demonstrate that in standard mobility models the individuals tend to diffuse
faster than what observed in reality, whereas the predictions of the adaptive
memory approach significantly agree with observations. We show that, as a
consequence, the incidence and the geographic spread of a disease could be
inadequately estimated when standard approaches are used, with crucial
implications on resources deployment and policy making during an epidemic
outbreak.
