Epidemic dynamics with non-Markovian travel in multilayer networks

In our modern time, travel has become one of the most significant factors contributing to global epidemic spreading. A deficiency in the literature is that travel has largely been treated as a Markovian process: it occurs instantaneously without any memory effect. To provide informed policies such as determining the mandatory quarantine time, the non-Markovian nature of real-world traveling must be taken into account. We address this fundamental problem by constructing a network model in which travel takes a finite time and infections can occur during the travel. We find that the epidemic threshold can be maximized by a proper level of travel, implying that travel infections do not necessarily promote spreading. More importantly, the epidemic threshold can exhibit a two-threshold phenomenon in that it can increase abruptly and significantly as the travel time exceeds a critical value. This may provide a quantitative estimation of the minimally required quarantine time in a pandemic.