Dataset Information

Power-law population heterogeneity governs epidemic waves.

ABSTRACT: We generalize the Susceptible-Infected-Removed (SIR) model for epidemics to take into account generic effects of heterogeneity in the degree of susceptibility to infection in the population. We introduce a single new parameter corresponding to a power-law exponent of the susceptibility distribution at small susceptibilities. We find that for this class of distributions the gamma distribution is the attractor of the dynamics. This allows us to identify generic effects of population heterogeneity in a model as simple as the original SIR model which is contained as a limiting case. Because of this simplicity, numerical solutions can be generated easily and key properties of the epidemic wave can still be obtained exactly. In particular, we present exact expressions for the herd immunity level, the final size of the epidemic, as well as for the shape of the wave and for observables that can be quantified during an epidemic. In strongly heterogeneous populations, the herd immunity level can be much lower than in models with homogeneous populations as commonly used for example to discuss effects of mitigation. Using our model to analyze data for the SARS-CoV-2 epidemic in Germany shows that the reported time course is consistent with several scenarios characterized by different levels of immunity. These scenarios differ in population heterogeneity and in the time course of the infection rate, for example due to mitigation efforts or seasonality. Our analysis reveals that quantifying the effects of mitigation requires knowledge on the degree of heterogeneity in the population. Our work shows that key effects of population heterogeneity can be captured without increasing the complexity of the model. We show that information about population heterogeneity will be key to understand how far an epidemic has progressed and what can be expected for its future course.

SUBMITTER: Neipel J

PROVIDER: S-EPMC7556502 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Power-law population heterogeneity governs epidemic waves.

Neipel Jonas J Bauermann Jonathan J Bo Stefano S Harmon Tyler T Jülicher Frank F

PloS one 20201014 10

We generalize the Susceptible-Infected-Removed (SIR) model for epidemics to take into account generic effects of heterogeneity in the degree of susceptibility to infection in the population. We introduce a single new parameter corresponding to a power-law exponent of the susceptibility distribution at small susceptibilities. We find that for this class of distributions the gamma distribution is the attractor of the dynamics. This allows us to identify generic effects of population heterogeneity ...[more]

PMID: 33052918

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Project description:There are two major sequencing technologies for investigating the microbiome: the amplicon sequencing that generates the OTU (operational taxonomic unit) tables of marker genes (e.g., bacterial 16S-rRNA), and the metagenomic shotgun sequencing that generates metagenomic gene abundance (MGA) tables. The OTU table is the counterpart of species abundance tables in macrobial ecology of plants and animals, and has been the target of numerous ecological and network analyses in recent gold rush for microbiome research and in great efforts for establishing an inclusive theoretical ecology. Nevertheless, MGA analyses have been largely limited to bioinformatics pipelines and ad hoc statistical methods, and systematic approaches to MGAs guided by classic ecological theories are still few. Here, we argue that, the difference between "gene kinds" and "gene species" are nominal, and the metagenome that a microbiota carries is essentially a 'community' of metagenomic genes (MGs). Each row of a MGA table represents a metagenome of a microbiota, and the whole MGA table represents a 'meta-metagenome' (or an assemblage of metagenomes) of N microbiotas (microbiome samples). Consequently, the same ecological/network analyses used in OTU analyses should be equally applicable to MGA tables. Here we choose to analyze the heterogeneity of metagenome by introducing classic Taylor's power law (TPL) and its recent extensions in community ecology. Heterogeneity is a fundamental property of metagenome, particularly in the context of human microbiomes. Recent studies have shown that the heterogeneity of human metagenomes is far more significant than that of human genomes. Therefore, without deep understanding of the human metagenome heterogeneity, personalized medicine of the human microbiome-associated diseases is hardly feasible. The TPL extensions have been successfully applied to measure the heterogeneity of human microbiome based on amplicon-sequencing reads of marker genes (e.g., 16s-rRNA). In this article, we demonstrate the analysis of the metagenomic heterogeneity of human gut microbiome at whole metagenome scale (with type-I power law extension) and metagenomic gene scale (type-III), as well as the heterogeneity of gene clusters, respectively. We further examine the influences of obesity, IBD and diabetes on the heterogeneity, which is of important ramifications for the diagnosis and treatment of human microbiome-associated diseases.

Project description:Spatial heterogeneity is a fundamental characteristic of organisms from viruses to humans. Measuring heterogeneity is challenging, especially for naked-eye invisible viruses, but of obvious importance. For example, spatial heterogeneity of virus distribution may strongly influence infection spreading and outbreaks in the case of pathogenic viruses; the spatial distribution (i.e., the inter-subject heterogeneity) of commensal viruses within/on our bodies can influence the competition, coexistence, and dispersal of viruses within or between our bodies. Taylor's power law (TPL) was first discovered in the 1960s to describe the spatial distributions of plant and/or animal populations, and since then it has been verified by numerous experimental and theoretical studies. Recently, TPL has been extended from population to community level and applied to bacterial communities. Here we report the first comprehensive testing of the TPL fitted to human virome datasets. It was found that the human virome follows the TPL as bacterial communities do. Furthermore, the TPL heterogeneity scaling parameter of human virome is virtually the same as that of the human bacterial microbiome (1.916 vs. 1.926). We postulate that the extreme closeness of human viruses and bacteria in heterogeneity scaling coefficients could be attributed to the fact that most of the viruses that were annotated in this study actually belong to bacteriophages (86% viral OTUs) that "piggyback" on their bacterial hosts, and their distributions are likely host-dependent. The scaling parameter, which measures the inter-subject heterogeneity changes, should be an innate property of human microbiomes including both bacteria and viruses. It is similar to the acceleration coefficient of the gravity (g = 9.8) as specified by Newton's law, which is invariant on the earth. Nevertheless, we caution that our postulation is contingent on an implicit assumption that the proportion of bacteriophages to total virome may not change significantly when more virus species can be identified in future.

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Power-law population heterogeneity governs epidemic waves.

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Power-law population heterogeneity governs epidemic waves.

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