A model of COVID-19 propagation based on a gamma subordinated negative binomial branching process: A tool for decision making with small populations

We build a parsimonious Crump-Mode-Jagers continuous time branching process of COVID-19 propagation based on a negative binomial process subordinated by a gamma subordinator. By focusing on the stochastic nature of the process in small populations, our model provides decision making insight into mitigation strategies as an outbreak begins. Our model accommodates contact tracing and isolation, allowing for comparisons between different types of intervention. We emphasize a physical interpretation of the disease propagation throughout which affords analytical results for comparison to simulations. Our model provides a basis for decision makers to understand the likely trade-offs and consequences between alternative outbreak mitigation strategies particularly in office environments and confined work-spaces. Combining the asymptotic limit of our model with Bayesian hierarchical techniques, we provide US county level inferences for the reproduction number from cumulative case count data over July and August of this year.

A large set of Finnish affected sibling pair families with type 2 diabetes suggests susceptibility loci on chromosomes 6, 11, and 14.

The aim of the Finland-United States Investigation of NIDDM Genetics (FUSION) study is to identify genes that predispose to type 2 diabetes or are responsible for variability in diabetes-related traits via a positional cloning and positional candidate gene approach. In a previously published genome-wide scan of 478 Finnish affected sibling pair (ASP) families (FUSION 1), the strongest linkage results were on chromosomes 20 and 11. We now report a second genome-wide scan using an independent set of 242 Finnish ASP families (FUSION 2), a detailed analysis of the combined set of 737 FUSION 1 + 2 families (495 updated FUSION 1 families), and fine mapping of the regions of chromosomes 11 and 20. The strongest FUSION 2 linkage results were on chromosomes 6 (maximum logarithm of odds score [MLS] = 2.30 at 95 cM) and 14 (MLS = 1.80 at 57 cM). For the combined FUSION 1 + 2 families, three results were particularly notable: chromosome 11 (MLS = 2.98 at 82 cM), chromosome 14 (MLS = 2.74 at 58 cM), and chromosome 6 (MLS = 2.66 at 96 cM). We obtained smaller FUSION 1 + 2 MLSs on chromosomes X (MLS = 1.27 at 152 cM) and 20p (MLS = 1.21 at 20 cM). Among the 10 regions that showed nominally significant evidence for linkage in FUSION 1, four (on chromosomes 6, 11, 14, and X) also showed evidence for linkage in FUSION 2 and stronger evidence for linkage in the combined FUSION 1 + 2 sample.