Epidemic Thresholds and Disease Dynamics in Metapopulations: The Role of Network Structure and Human Mobility

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 2, Page 1579-1609, June 2024.
Abstract.We calculate epidemic thresholds and investigate the dynamics of a disease in a networked metapopulation. To study the specific role of mobility levels, we utilize the SIR-network model and consider a range of network structures. For star-shaped networks where all nodes only connect to a center, we obtain the same epidemic threshold formulas as previously found for fully connected networks, considering all nodes with the same infection rate except one. We thus create a new terminology by saying that fully connected and star-shaped networks have the Standard Threshold Property. Next, we analyze cycle-shaped networks, which yield epidemic thresholds different from those obtained using star-shaped networks. We then analyze more general classes of networks by combining the star, cycle, and other structures, obtaining classes of networks with the Standard Threshold Property. We present some conjectures on even more flexible networks and complete our analysis by presenting simulations to explore the epidemic dynamics for the different structures.