During the COVID-19 pandemic, many countries implemented international travel restrictions that aimed to contain viral spread while still allowing necessary cross-border travel for social and economic reasons. The relative effectiveness of these approaches for controlling the pandemic has gone largely unstudied. Here we developed a flexible network meta-population model to compare the effectiveness of international travel policies, with a focus on evaluating the benefit of policy coordination. Because country-level epidemiological parameters are unknown, they need to be estimated from data; we accomplished this using approximate Bayesian computation, given the nature of our complex stochastic disease transmission model. Based on simulation and theoretical insights we find that, under our proposed policy, international airline travel may resume up to 58% of the pre-pandemic level with pandemic control comparable to that of a complete shutdown of all airline travel. Our results demonstrate that global coordination is necessary to allow for maximum travel with minimum effect on viral spread.

Cattle are natural hosts of the intracellular pathogen, Brucella abortus, which inflicts a significant burden on the health and reproduction of these important livestock. The primary routes of infection in field settings have been described, but it is not known how the bovine host shapes the structure of B. abortus populations during infection. We utilized a library of approximately 106 uniquely barcoded B. abortus strains to temporally and spatially quantify population structure at the strain level during colonization of cattle through a natural route of infection. Introducing 108 bacteria from this barcoded library to the conjunctival mucosa resulted in expected levels of local lymph node colonization at a one-week timepoint. We leveraged variance in strain abundance in the library to demonstrate that only 1 in 10,000 brucellae introduced at the site of infection reached the parotid lymph nodes. Thus, cattle restrict the overwhelming majority of B. abortus introduced via the ocular conjunctiva at this dose. Individual strains were spatially restricted within the host tissue, and the total B. abortus census was dominated by a small number of distinct strains in each lymph node. These results define a bottleneck that B. abortus must traverse to colonize local lymph nodes from the conjunctival mucosa. The data further support a model in which a small number of spatially isolated granulomas founded by unique strains are present one-week post infection. These experiments demonstrate the power of barcoded transposon tools to quantify infection bottlenecks and to define pathogen population structure in host tissues.Significance statementUnderstanding microbial population dynamics during infection has important implications for disease management, transmission and pathogen evolution. A quantitative analysis of microbial population structure requires the ability to track individual strains. We used a pool of individually barcoded strains to measure changes in Brucella abortus population structure during infection of bovine hosts via the ocular conjunctiva, a natural route of entry. Cattle exert a severe bottleneck on the bacterial population entering through the conjunctival mucosa such that individual cells have a 0.0001 probability of colonizing a local draining lymph node. The populations in lymph nodes, even on different sides of the same animal, are distinct and dominated by a small number of highly abundant, spatially distinct clones.

Cattle are natural hosts of the intracellular pathogen Brucella abortus, which inflicts a significant burden on the health and reproduction of these important livestock. The primary routes of infection in field settings have been described, but it is not known how the bovine host shapes the structure of B. abortus populations during infection. We utilized a library of uniquely barcoded B. abortus strains to temporally and spatially quantify population structure during colonization of cattle through a natural route of infection. Introducing 108 bacteria from this barcoded library to the conjunctival mucosa resulted in expected levels of local lymph node colonization at a 1-wk time point. We leveraged variance in strain abundance in the library to demonstrate that only 1 in 10,000 brucellae introduced at the site of infection reached a parotid lymph node. Thus, cattle restrict the overwhelming majority of B. abortus introduced via the ocular conjunctiva at this dose. Individual strains were spatially restricted within the host tissue, and the total B. abortus census was dominated by a small number of distinct strains in each lymph node. These results define a bottleneck that B. abortus must traverse to colonize local lymph nodes from the conjunctival mucosa. The data further support a model in which a small number of spatially isolated granulomas founded by unique strains are present at 1 wk postinfection. These experiments demonstrate the power of barcoded transposon tools to quantify infection bottlenecks and to define pathogen population structure in host tissues.

A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high‐dimensional settings. We propose a simple estimator of the precision matrix based on the connection between the known graphical structure and the precision matrix. We obtain the rates of convergence of the proposed estimators and derive the asymptotic normality of the proposed estimator in the high‐dimensional setting when the data dimension grows with the sample size. Numerical simulations are conducted to demonstrate the performance of the proposed method. We also show that the proposed method outperforms some existing methods that do not utilize the graphical structure information.