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Using active matter to introduce spatial heterogeneity to the susceptible infected recovered model of epidemic spreading.

ABSTRACT: The widely used susceptible-infected-recovered (S-I-R) epidemic model assumes a uniform, well-mixed population, and incorporation of spatial heterogeneities remains a major challenge. Understanding failures of the mixing assumption is important for designing effective disease mitigation approaches. We combine a run-and-tumble self-propelled active matter system with an S-I-R model to capture the effects of spatial disorder. Working in the motility-induced phase separation regime both with and without quenched disorder, we find two epidemic regimes. For low transmissibility, quenched disorder lowers the frequency of epidemics and increases their average duration. For high transmissibility, the epidemic spreads as a front and the epidemic curves are less sensitive to quenched disorder; however, within this regime it is possible for quenched disorder to enhance the contagion by creating regions of higher particle densities. We discuss how this system could be realized using artificial swimmers with mobile optical traps operated on a feedback loop.

SUBMITTER: Forgacs P

PROVIDER: S-EPMC9253087 | biostudies-literature | 2022 Jul

REPOSITORIES: biostudies-literature

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Using active matter to introduce spatial heterogeneity to the susceptible infected recovered model of epidemic spreading.

Forgács P P Libál A A Reichhardt C C Hengartner N N Reichhardt C J O CJO

Scientific reports 20220704 1

The widely used susceptible-infected-recovered (S-I-R) epidemic model assumes a uniform, well-mixed population, and incorporation of spatial heterogeneities remains a major challenge. Understanding failures of the mixing assumption is important for designing effective disease mitigation approaches. We combine a run-and-tumble self-propelled active matter system with an S-I-R model to capture the effects of spatial disorder. Working in the motility-induced phase separation regime both with and wi ...[more]

PMID: 35787642

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Project description:We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which represents a generalization of degree-ordered percolation, we derive a scaling solution on uncorrelated complex networks, unveiling the existence of diverse mechanisms leading to the formation of a percolating cluster. The scaling solution accurately reproduces universal properties of the transition. This finding is used to infer the critical properties of the susceptible-infected-susceptible model for epidemics in infinite and finite power-law distributed networks. Here, discrepancies between analytical approaches and numerical results regarding the finite-size scaling of the epidemic threshold are a crucial open issue in the literature. We find that the scaling exponent assumes a nontrivial value during a long preasymptotic regime. We calculate this value, finding good agreement with numerical evidence. We also show that the crossover to the true asymptotic regime occurs for sizes much beyond currently feasible simulations. Our findings allow us to rationalize and reconcile all previously published results (both analytical and numerical), thus ending a long-standing debate. Summary Complex networks represent the interaction pattern for many real-world phenomena such as epidemic spreading. The simplest and most fundamental model for the diffusion of infectious diseases without acquired immunity predicts a vanishing epidemic threshold in the limit of large systems. In other words, no matter how small the infectiousness of the disease, there is always a finite fraction of the overall population which is infected for long times. So far, the detailed mechanism underlying this phenomenology has remained unclear. Here, we provide a complete and quantitative understanding of the model’s behavior. While the role of hubs (individuals with high connectivity) was already believed to be important, we fully clarify its nature, pointing out the highly nontrivial interplay among hubs. Each hub acts as an infection hotbed and the global epidemic emerges from hubs reinfecting each other. Surprisingly, this mechanism is at work even when the hubs are not in direct mutual contact but transmit the infection through chains of low-connectivity individuals. The survival of the epidemic is then a manifestation of a novel, long-range, percolation process among distant hubs, whose properties explain the behavior of the epidemic model. These findings rationalize and reconcile previously published results and point out long-range indirect interactions as potentially crucial ingredients for other collective phenomena in networked systems.

Dataset Information

Using active matter to introduce spatial heterogeneity to the susceptible infected recovered model of epidemic spreading.

Publications

Using active matter to introduce spatial heterogeneity to the susceptible infected recovered model of epidemic spreading.

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