Critical behaviors of nonlinear contagion models with recurrent mobility patterns

Recently, there has been a lot of discussion about the nonlinearity property of contagion processes in epidemic spreading on social networks with various structures. In this paper, we propose a nonlinear contagion model in networked metapopulations to investigate the critical behavior of epidemics with recurrent mobility patterns. First, we build up a discrete-time Markovian chain model to formulate the spreading of susceptible-infected-susceptible-like diseases. Additionally, we develop a practicable framework to analyze the impact of mobility on the epidemic threshold and derive the theoretical condition for the transition of an epidemic from a local to a global scale. This transition is associated with multiple discontinuous phase changes. We validate our analytical results through extensive numerical simulations on both regular and heterogeneous networks. Our findings offer a useful tool to discuss the implementation of prevention strategies such as quarantine and lockdown.