Power-law population heterogeneity governs epidemic waves

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

Using noninvasive metagenomics to characterize viral communities from wildlife

Microbial communities play an important role in organismal and ecosystem health. While high‐throughput metabarcoding has revolutionized the study of bacterial communities, generating comparable viral communities has proven elusive, particularly in wildlife samples where the diversity of viruses and limited quantities of viral nucleic acid present distinctive challenges. Metagenomic sequencing is a promising solution for studying viral communities, but the lack of standardized methods currently precludes comparisons across host taxa or localities. Here, we developed an untargeted shotgun metagenomic sequencing protocol to generate comparable viral communities from noninvasively collected faecal and oropharyngeal swabs. Using samples from common vampire bats (Desmodus rotundus), a key species for virus transmission to humans and domestic animals, we tested how different storage media, nucleic acid extraction procedures and enrichment steps affect viral community detection. Based on finding viral contamination in foetal bovine serum, we recommend storing swabs in RNAlater or another nonbiological medium. We recommend extracting nucleic acid directly from swabs rather than from supernatant or pelleted material, which had undetectable levels of viral RNA. Results from a low‐input RNA library preparation protocol suggest that ribosomal RNA depletion and light DNase treatment reduce host and bacterial nucleic acid, and improve virus detection. Finally, applying our approach to twelve pooled samples from seven localities in Peru, we showed that detected viral communities saturated at the attained sequencing depth, allowing unbiased comparisons of viral community composition. Future studies using the methods outlined here will elucidate the determinants of viral communities across host species, environments and time