Memory-induced complex contagion in epidemic spreading

Abstract

Albeit epidemic models have evolved into powerful predictive tools for the spread of diseases and opinions, most assume memoryless agents and independent transmission channels. We develop an infection mechanism that is endowed with memory of past exposures and simultaneously incorporates the joint effect of multiple infectious sources. Analytic equations and simulations of the susceptible-infected-susceptible model in unstructured substrates reveal the emergence of an additional phase that separates the usual healthy and endemic ones. This intermediate phase shows fundamentally distinct characteristics, and the system exhibits either excitability or an exotic variant of bistability. Moreover, the transition to endemicity presents hybrid aspects. These features are the product of an intricate balance between two memory modes and indicate that non-Markovian effects significantly alter the properties of spreading processes.

Explicit non-Markovian susceptible-infected-susceptible mean-field epidemic threshold for Weibull and Gamma infections but Poisson curings

“…That result is partly verified in Ref. [14] by an independent simulation, based on Ref. [15] and revisited here in Sec.…”

Coevolution spreading in complex networks

“…When α > α c the steady-state density of the infected nodes exhibits explosive growth with respect to the basic transmission rate and a hysteresis loop emerges. Hoffmann and Boguñá [211] proposed a synergistic cumulative contagion model, which takes into account the memory of past exposures and incorporates the synergy effects of multiple infectious sources. They found that the interplay of the non-Markovian feature and a complex contagion produces rich phenomena, including the loss of universality, collective memory loss, bistable regions, hysteresis loops, and excitable phases.…”

Non-Markovian epidemic spreading on temporal networks

“…Interestingly, non-Markovian effects in recovery processes can also make the network more resilient against large-scale failures [28] and, in some cases, it has been demonstrated that non-Markovian dynamics can be reduced to Markovian dynamics, simplifying the modeling process [24,26,29]. Finally, non-Markovian dynamics may induce an effective complex contagion mechanism, with correlated infectious channels, leading to the appearance of novel exotic epidemic phases [30].…”