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Host mobility plays a fundamental role in the spatial spread of infectiousdiseases. Previous theoretical works based on the integration of network theoryinto the metapopulation framework have shown that the heterogeneities thatcharacterize real mobility networks favor the propagation of epidemics.Nevertheless, the studies conducted so far assumed the mobility process to beeither Markovian or non-Markovian with a fixed traveling time scale. Availablestatistics however show that the time spent by travelers at destination ischaracterized by wide fluctuations, ranging between a single day up to severalmonths. Such varying length of stay crucially affects the chance and durationof mixing events among hosts and may therefore have a strong impact on thespread of an emerging disease. Here, we present an analytical and computationalstudy of epidemic processes on a complex subpopulation network where travelershave memory of their origin and spend a heterogeneously distributed timeinterval at their destination. Through analytical calculations and numericalsimulations we show that the heterogeneity of the length of stay alters theexpression of the threshold between local outbreak and global invasion, and,moreover, it changes the epidemic behavior of the system in case of a globaloutbreak. Additionally, our theoretical framework allows us to study the effectof changes in the traveling behavior in response to the infection, byconsidering a scenario in which sick individuals do not leave their homelocation. Finally, we compare the results of our non-Markovian framework withthose obtained with a classic Markovian approach and find relevant differencesbetween the two, in the estimate of the epidemic invasion potential, as well asof the timing and the pattern of its spatial spread.

Human mobility and time spent at destination: Impact on spatial epidemic spreading