The Effects of Evolutionary Adaptations on Spreading Processes in Complex Networks

TL;DR

This paper develops a mathematical framework to analyze how evolution impacts epidemic thresholds, sizes, and probabilities in complex networks, highlighting limitations of classical models and exploring co-infection effects.

Contribution

It introduces a new theory incorporating evolutionary dynamics into epidemic modeling on networks, improving prediction accuracy and revealing key differences from classical models.

Findings

Classical models predict epidemic size and threshold well but fail on emergence probability.

Evolution significantly alters epidemic dynamics and phase transition order.

Co-infection can change the phase transition from second to first order.

Abstract

A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution. However, in real-life spreading processes, pathogens often evolve in response to changing environments and medical interventions and information is often modified by individuals before being forwarded. In this paper, we investigate the evolution of spreading processes on complex networks with the aim of i) revealing the role of evolution on the threshold, probability, and final size of epidemics; and ii) exploring the interplay between the structural properties of the network and the dynamics of evolution. In particular, we develop a mathematical theory that accurately predicts the epidemic threshold and the expected epidemic size as functions of the characteristics of the spreading process, the evolutionary dynamics of the pathogen, and the structure of the underlying contact network. In addition to the mathematical theory, we perform extensive simulations on random and real-world contact networks to verify our theory and reveal the significant shortcomings of the classical mathematical models that do not capture evolution. Our results reveal that the classical, single-type bond-percolation models may accurately predict the threshold and final size of epidemics, but their predictions on the probability of emergence are inaccurate on both random and real-world networks. This inaccuracy sheds the light on a fundamental disconnect between the classical bond-percolation models and real-life spreading processes that entail evolution. Finally, we consider the case when co-infection is possible and show that co-infection could lead the order of phase transition to change from second-order to first-order.