Epidemic spreading in random walkers with heterogeneous interaction radius

We study epidemic spreading in a random walk network where agents with heterogeneous interaction radius randomly walk in a planar space. We obtain the explicit expression of epidemic threshold which indicates that the heterogeneity of interaction radius decreases the threshold. Concretely, the greater the variance of the radius distribution is, the smaller the epidemic threshold will be. Simulation results about the epidemic threshold match well with our theoretical results. In simulation study, the infection density in steady state, which is called the final density, is investigated. When there are two different values of radius, a larger mean value of radius increases the final density. However, although an increasing second order origin moment of radius makes the epidemic easier to outbreak, it also lowers the final density of infected individuals.