Summary: We consider an epidemical model within socially interacting mobile individuals to study the behaviors of steady states of epidemic propagation in 2D networks. Using mean-field approximation and large scale simulations, we recover the usual epidemic behavior with critical thresholds \(\delta c\) and \(pc\) below which infectious disease dies out. For the population density \(\delta \) far above \(\delta c\), it is found that there is linear relationship between contact rate \(\lambda \) and the population density \(\delta \) in the main. At the same time, the result obtained from mean-field approximation is compared with our numerical result, and it is found that these two results are similar by and large but not completely the same.