Virus propagation: threshold conditions for multiple profile networks

Imagine that we have a highly competing virus that is spreading over a (e.g., social) network where users have different sensitivity/interest against it. A virus may be anything that has a “spreading” behavior such as a rumor, a social media trend or even an infectious disease. Is it possible to predict the outcome in such a viral phenomenon and compute the number of users that will eventually get infected? We answer this question by providing qualitative and quantitative thresholds that describe the behavior of the virus in a given network. Our main contribution is that for the first time, the case of a heterogeneous (with respect to the nodes) network is analytically tackled. We model the different sensitivity to the virus by dividing the nodes of the network into different groups. Each group has a particular profile describing its behavior toward the virus. Conditions are provided based on certain network characteristics that govern the extent of the infection. These conditions are experimentally verified by extensive experiments.