Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2010.04942

Contact Tracing & Super-Spreaders in the Branching-Process Model

Johannes Müller·Volker Hösel
View original source ↗Read source document ↗Export metadata ↓

Abstract

In recent years, it became clear that super-spreader events play an important role, particularly in the spread of airborne infections. We investigate a novel model for super-spreader events, not based on a heterogeneous contact graph but on a random contact rate: Many individuals become infected synchronously in single contact events. We use the branching-process approach for contact tracing to analyze the impact of super-spreader events on the effect of contact tracing. Here we neglect a tracing delay. Roughly speaking, we find that contact tracing is more efficient in the presence of super-spreaders if the fraction of symptomatics is small, the tracing probability is high, or the latency period is distinctively larger than the incubation period. In other cases, the effect of contact tracing can be decreased by super-spreaders. Numerical analysis with parameters suited for SARS-CoV-2 indicates that super-spreaders do not decrease the effect of contact tracing crucially in case of that infection.

Explore related subjects

q-bio.PEphysics.soc-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Johannes Müller, Volker Hösel. 2021-04-10. Contact Tracing & Super-Spreaders in the Branching-Process Model. https://arxiv.org/abs/2010.04942

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Evolution as fitness landscape navigation: concepts, measures, and emerging questions

Fitness landscapes are mappings between genotypes, phenotypes, and fitness that shape evolution. In recent years, empirical work and theoretical models have greatly advanced our understanding of how populations navigate rugged fitness landscapes. Here, we provide a timely review of the theoretical aspects of this field. Its rapidly growing literature employs a wide range of terms, which are sometimes used ambiguously or inconsistently. We therefore begin by defining the major concepts and the field's vocabulary, highlighting our own terminology choices wherever needed. We then review key results on the relationships between epistasis, ruggedness, accessibility, and navigability for genotype-fitness maps, highlighting several complex and sometimes counterintuitive connections that have emerged. Further, we review how the conserved structural properties of the underlying genotype-phenotype map, which can lead to the formation of large connected neutral networks of genotypes, influence dynamics on fitness landscapes. We then compare the two levels to study landscape navigation: the level of genotype-phenotype maps and the level of genotype-fitness maps. Our review leads us to propose a new measure of navigability, based on evolutionary outcomes, that is broadly applicable and overcomes limitations of existing measures. Finally, we highlight examples from the smaller body of work that relaxes the common assumption of fitness-monotonic paths on static landscapes, and discuss how this can fundamentally change the nature of fitness landscape navigation. Throughout the review, we identify directions for future work to fill existing gaps and to synthesize the disparate strands of research within the field.

q-bio.PE↗
arXiv2026

Best Matches in Phylogenetic Networks

Best match graphs (BMGs) were introduced in mathematical phylogenetics to describe the concept of closest relatives for related genes (leaves of rooted tree) in different organisms (defining leaf colors). We generalize this concept here to leaf-colored rooted networks, where least common ancestors are in general neither unique nor comparable. We characterize BMGs of rooted networks as those vertex-colored digraphs that are properly colored and satisfy an easy-to-check condition that we call the sicor-in-hub property. BMGs can be recognized in linear time and an explaining network can be constructed in quadratic time. Analogous results are obtained for reciprocal best match graphs (RBMGs), where an edge $\{x,y\}$ corresponds to pairs of vertices with different color that are mutually closest relatives.

q-bio.PE↗
arXiv2026

Exact Counts of Binary Phylogenetic Networks with Four Reticulations

Phylogenetic networks provide a flexible framework for representing reticulate evolutionary processes, such as hybridization, introgression, recombination, and horizontal gene transfer. However, their combinatorial complexity makes even basic enumeration problems difficult. Building on our previous work for networks with up to three reticulations, we derive an explicit closed-form formula for the number of unrestricted rooted binary phylogenetic networks with four reticulations on \(n\) labeled taxa. Our approach is based on tree-component graphs. We classify the 79 possible component graphs corresponding to networks with four reticulations into ten groups. We then enumerate the networks associated with each group by combining known counts of one-component networks, forests, and networks with fewer reticulations. Summing these contributions yields the desired formula. This result extends the exact enumeration of unrestricted binary phylogenetic networks to four reticulations and further demonstrates the effectiveness of component graphs for systematically organizing and counting increasingly complex network classes.

q-bio.PE↗