Pattern dynamics of interacting contagions

TL;DR

This paper investigates how two interacting contagions spread in space, revealing complex pattern formations, hysteresis effects, and challenges in eradication due to spatial and interaction dynamics.

Contribution

It introduces a spatial contagion model with interacting agents, uncovering novel pattern dynamics and hysteresis phenomena not seen in single-agent or non-spatial models.

Findings

Nontrivial spatial infection patterns emerge under specific movement and interaction conditions.

Pattern hysteresis occurs, affecting infection eradication efforts.

Spatial dynamics significantly increase the difficulty of eradicating infections.

Abstract

The spread of infectious diseases, rumors, fashions, innovations are complex contagion processes, embedded both in networked and spatial contexts. Here we investigate the pattern dynamics of a complex contagion, where two agents, say $A$ and $B$, interact with each other and diffuse simultaneously in the geographic space. The contagion process for each follows the classical susceptible-infected-susceptible kinetics, and their interaction introduces a potential change in the secondary infection propensity compared to the baseline reproduction ratio $R_0$. We show that nontrivial spatial infection patterns arise, when the susceptible move faster than the infected and the interaction between the two agents is neither too competitive nor too cooperative. Interestingly, the system exhibits pattern hysteresis phenomena that quite different parameter regions allowing for patterns exist in the direction of increasing $R_0$ and in the direction of eradication by its reduction. The latter shows a remarkable enhancement in the contagion prevalence, meaning that the infection eradication now becomes extremely difficult compared to the single-agent scenario and to the coinfection without space. Linearization analysis supports our observations, and we identified the required elements and dynamical mechanism behind the emergence of a pattern. These findings call for further investigation for their close relevance, both in biological and social contagions.