Spatial epidemiology of networked metapopulation: An overview

Lin WANG; Xiang Li

It might be infeasible to analyze the non-Markovian properties of human commuting with previous reaction-diffusion theory. In this regard, Balcan and Vespignani [91] extended the metapopulation framework by considering the impact of human recurrent commuting, which assumes that individuals remember their subpopulations of residence, with a constraint that commuters staying at their destination subpopulations cannot continue moving to other places but return to the residences with a certain rate. The approach of timescale separation is applied to perform theoretical analysis, since in reality the number of frequent commuters only accounts for a small fraction of local populations. This leads to a mean-field description of stationary populations distribution. Generalizing the theory of branching process, Balcan and Vespignani [97] obtained the global invasion threshold for the reaction-commuting networked metapopulation systems, which establishes a new threshold relevant to the typical visiting duration of commuters. With a high return rate, the sojourn time (i.e., length of stay) of infected commuters might be too short to transmit the infection to susceptibles in adjacent unaffected subpopulations.