This paper addresses the propagation of computer viruses in real networks, focusing on the epidemic threshold and the time it takes to disinfect a network. The authors propose a new analytic model that accurately models virus propagation in any network, including real and synthetic graphs. They introduce a general epidemic threshold condition that applies to arbitrary graphs, relating the threshold to the largest eigenvalue of the adjacency matrix. The model is shown to be more precise and general than previous models, and it predicts that infections tend to zero exponentially below the epidemic threshold. The paper also demonstrates the model's accuracy through extensive experiments on real and synthetic graphs, including homogeneous, Barabási-Albert (BA) power-law, and Erdős-Rényi networks. The authors further show that their threshold condition holds for various graph types, such as infinite power-law graphs, and provides insights into phase transition phenomena at the epidemic threshold.This paper addresses the propagation of computer viruses in real networks, focusing on the epidemic threshold and the time it takes to disinfect a network. The authors propose a new analytic model that accurately models virus propagation in any network, including real and synthetic graphs. They introduce a general epidemic threshold condition that applies to arbitrary graphs, relating the threshold to the largest eigenvalue of the adjacency matrix. The model is shown to be more precise and general than previous models, and it predicts that infections tend to zero exponentially below the epidemic threshold. The paper also demonstrates the model's accuracy through extensive experiments on real and synthetic graphs, including homogeneous, Barabási-Albert (BA) power-law, and Erdős-Rényi networks. The authors further show that their threshold condition holds for various graph types, such as infinite power-law graphs, and provides insights into phase transition phenomena at the epidemic threshold.