SIS Process with Heterogeneous Infection Rates in Wheel Graphs

The studies in epidemic-like processes have drawn much attention for the last decades. Structural or dynamical heterogeneity has been reported to have great impact on the statistical properties of the epidemic dynamics. In this work, we investigate the susceptible-infected-susceptible (SIS) process with heterogeneous infection and curing rates in wheel graphs. Specifically, the wheel graph is composed of a center node with one infection setting while the others are with another infection setting. We first apply an individual-based mean-field approximation framework to model and analyze the concerned SIS process in wheel graphs. We derive the approximate solutions of the steady-state fraction of infected nodes as well as the epidemic threshold. We conduct simulations to verify the proposed theories. This work has the potential to expand our understanding of the complex impact of dynamical and structural heterogeneity over dynamics of epidemic-like processes.