The Effects of Evolutionary Adaptations on Spreading Processes in\n Complex Networks

A common theme among the proposed models for network epidemics is the\nassumption that the propagating object, i.e., a virus or a piece of\ninformation, is transferred across the nodes without going through any\nmodification or evolution. However, in real-life spreading processes, pathogens\noften evolve in response to changing environments and medical interventions and\ninformation is often modified by individuals before being forwarded. In this\npaper, we investigate the evolution of spreading processes on complex networks\nwith the aim of i) revealing the role of evolution on the threshold,\nprobability, and final size of epidemics; and ii) exploring the interplay\nbetween the structural properties of the network and the dynamics of evolution.\nIn particular, we develop a mathematical theory that accurately predicts the\nepidemic threshold and the expected epidemic size as functions of the\ncharacteristics of the spreading process, the evolutionary dynamics of the\npathogen, and the structure of the underlying contact network. In addition to\nthe mathematical theory, we perform extensive simulations on random and\nreal-world contact networks to verify our theory and reveal the significant\nshortcomings of the classical mathematical models that do not capture\nevolution. Our results reveal that the classical, single-type bond-percolation\nmodels may accurately predict the threshold and final size of epidemics, but\ntheir predictions on the probability of emergence are inaccurate on both random\nand real-world networks. This inaccuracy sheds the light on a fundamental\ndisconnect between the classical bond-percolation models and real-life\nspreading processes that entail evolution. Finally, we consider the case when\nco-infection is possible and show that co-infection could lead the order of\nphase transition to change from second-order to first-order.\n