Abstract
Abstract : We study the emergence of global behavior in large scale networks. The underlying motivating application is epidemics like computer virus spreading, for example, in wide campus local networks. We consider multiple classes of viruses, each type bearing their own statistical characterization -- exogenous contamination, contagious propagation, and healing. The network state (distribution of nodes infected by each class in the network) is a jump Markov process, not necessarily reversible, making it a challenge to obtain its invariant distribution. By suitable renormalization, in the limit of a large network (number of nodes), we describe the macroscopic or emergent behavior of the network by the solution of a set of deterministic nonlinear differential equations. These nonlinear differential equations are obtained by mean field analysis of the microscopic random dynamics. We study the qualitative behavior of the nonlinear differential equations describing the mean field dynamics.
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