Epidemic dynamics with non-Markovian infection processes in metapopulation networks

Despite intensive studies on epidemic spreading in metapopulation networks, the infection process is normally assumed to be a Markovian process without considering time-dependent infectivity. In this paper, a reaction-diffusion SIRS epidemic model with non-Markovian infection processes is constructed on metapopulation networks, where the infection rate function associated with the sojourn time in the infected state is obtained by constructing the generation time distribution of the emerging infection process. Meanwhile, the recurrent mobility patterns are incorporated by the metapopulation model. By Lyapunov stability analysis, the epidemic outbreak condition is derived theoretically. The results show that the non-Markovian infection characteristics can significantly alter the transient behavior of epidemic spreading under the same basic reproduction number. Furthermore, with the increase in the average time for an infected individual to generate secondary cases in the non-Markovian process, the impact of mobility rate on transient epidemic spreading behavior will be reduced. Finally, mobility can have a suppressing effect on epidemic spreading dynamics when the population distribution exhibits significant asymmetry. The results can sharpen our understanding of the role of real-world non-Markovian infection processes in epidemic outbreaks.