Epidemic spreading model and stability of the networks in mobile environment

Abstract

In this paper, considering the random motion of nodes, we propose an epidemic spreading model on network of mobile environment based on the mean-filed theory. Using the theory of differential dynamical system, the behaviors of epidemic spreading are further analyzed. It is shown that if R0 1, the epidemic always dies out and the disease-free equilibrium is globally asymptotically stable; and if R0 1, the epidemic is uniformly persistent and the endemic equilibrium is globally asymptotically stable. Numerical simulations are given to validate the results of theoretical analysis.