Epidemic spreading of random walkers in metapopulation model on an alternating graph

Abstract Much literature exists on temporal networks for epidemic spreading. We present a metapopulation dynamic model on a temporal network; a subpopulation (patch) is represented by a node on a graph, and a link represents a migration path between patches. We consider the alternating graph as a temporal network. It alternates between star and complete graphs, where the nodes do not change but links vary temporally and periodically. Mobile individuals move by random walk through a link between nodes. Each individual is either susceptible (S) or infected (I). The reaction–diffusion equations are presented as ordinary differential equations with time-dependent coefficients. To evaluate the infection risk of each patch (node), we obtain the solutions of reaction–diffusion equations numerically. The temporal behavior of infected individuals depends highly on the frequency of the alternating graph. At low frequency, infected densities exhibit an oscillating behavior, while they keep a constant value at high frequencies. The crossover occurs from the oscillating state to the frozen state with increasing frequency. The SIS epidemic threshold is derived for the alternating graph. The epidemic threshold is lower than that on the star graph and higher than that on the complete graph.