Mean-field equations and stable behaviour in an epidemic model of mobile individuals

Epidemic propagation within socially interacting mobile individuals is investigated on a two-dimensional (2D) square lattice. The influence of these parameters (the automata density δ, the jumping probability p, etc) on epidemic spreading is studied, and the critical jumping probability pc and the critical population density δc are observed. Moreover, we establish the mean-field (MF) equations which are in good agreement with our network model. Here the efficient contact rate λ is not a constant but a function of the population density δ, the point is different with conventional MF equations. Through an approximate equivalence relation between network model and MF equations, the concrete form λ = f(δ) is obtained.