Bayesian Inference of State-Level COVID-19 Basic Reproduction Numbers across the United States

Although many persons in the United States have acquired immunity to COVID-19, either through vaccination or infection with SARS-CoV-2, COVID-19 will pose an ongoing threat to non-immune persons so long as disease transmission continues. We can estimate when sustained disease transmission will end in a population by calculating the population-specific basic reproduction number , the expected number of secondary cases generated by an infected person in the absence of any interventions. The value of relates to a herd immunity threshold (HIT), which is given by . When the immune fraction of a population exceeds this threshold, sustained disease transmission becomes exponentially unlikely (barring mutations allowing SARS-CoV-2 to escape immunity). Here, we report state-level estimates obtained using Bayesian inference. Maximum a posteriori estimates range from 7.1 for New Jersey to 2.3 for Wyoming, indicating that disease transmission varies considerably across states and that reaching herd immunity will be more difficult in some states than others. estimates were obtained from compartmental models via the next-generation matrix approach after each model was parameterized using regional daily confirmed case reports of COVID-19 from 21 January 2020 to 21 June 2020. Our estimates characterize the infectiousness of ancestral strains, but they can be used to determine HITs for a distinct, currently dominant circulating strain, such as SARS-CoV-2 variant Delta (lineage B.1.617.2), if the relative infectiousness of the strain can be ascertained. On the basis of Delta-adjusted HITs, vaccination data, and seroprevalence survey data, we found that no state had achieved herd immunity as of 20 September 2021.

On the correlation and sensitivity of so far statistical randomness tests based on runs

Abstract—Random numbers play a very important role in cryptography. More precisely, almost cryptographic primitives are ensured their security based on random values such as random key, nonces, salts... Therefore, the assessment of randomness according to statistical tests is really essential for measuring the security of cryptographic algorithms. In this paper, we focus on so far randomness tests based on runs in the literature. First, we have proved in detail that the expected number of gaps (or blocks) of length in a random sequence of length is . Secondly, we have evaluated correlation of some tests based on runs so far using Pearson coefficient method [5, 6] and Fail-Fail ratio one [7, 8]. Surprisingly, the Pearson coefficient method do not show any strong linear correlation of these runs-based tests but the Fail-Fail ratio do. Then, we have considered the sensitivity of these runs tests with some basic transformations. Finally, we have proposed some new runs tests based on the sensitivity results and applied evaluations to some random sources. Tóm tắt—Số ngẫu nhiên đóng một vai trò quan trọng trong mật mã. Cụ thể, độ an toàn của hầu hết các nguyên thủy mật mã đều được đảm bảo dựa trên các giá trị ngẫu nhiên như khóa, nonce, salt… Do đó, việc đánh giá tính ngẫu nhiên dựa trên các kiểm tra thống kê là thực sự cần thiết để đo độ an toàn cho các thuật toán mật mã. Trong bài báo này, chúng tôi tập trung vào các kiểm tra ngẫu nhiên dựa vào run trong các tài liệu. Đầu tiên, chúng tôi chứng minh chi tiết rằng kỳ vọng số các gap (khối) độ dài trong một chuỗi ngẫu nhiên độ dài là . Sau đó, chúng tôi đánh giá mối tương quan của một số kiểm tra dựa vào run bằng phương pháp hệ số Pearson [5, 6] và tỷ số Fail-Fail [7, 8]. Đáng ngạc nhiên là phương pháp hệ số Pearson không cho thấy bất kỳ mối tương quan tuyến tính mạnh nào của các kiểm tra dựa vào run, trong khi đó tỷ số Fail-Fail lại chỉ ra. Tiếp theo, chúng tôi xem xét độ nhạy của các kiểm tra run này với một số phép biến đổi cơ bản. Cuối cùng, chúng tôi đề xuất một số kiểm tra run mới dựa trên các kết quả độ nhạy và đánh giá áp dụng chúng cho một số nguồn ngẫu nhiên.

Assessing excess mortality in Vienna and Austria after the first year of the COVID-19 pandemic

In Austria, the first confirmed COVID-19 death occurred in early March 2020. Since then, the question as to whether and, if so, to what extent the COVID-19 pandemic has increased overall mortality has been raised in the public and academic discourse. In an effort to answer this question, Statistics Vienna (City of Vienna, Department for Economic Affairs, Labour and Statistics) has evaluated the weekly mortality trends in Vienna, and compared them to the trends in other Austrian provinces. For our analysis, we draw on data from Statistics Austria and the Austrian Agency for Health and Food Safety (AGES), which are published along with data on the actual and the expected weekly numbers of deaths via the Vienna Mortality Monitoring website. Based on the definition of excess mortality as the actual number of reported deaths from all causes minus the expected number of deaths, we calculate the weekly prediction intervals of the expected number of deaths for two age groups (0 to 64 years and 65 years and older). The temporal scope of the analysis covers not only the current COVID-19 pandemic, but also previous flu seasons and summer heat waves. The results show the actual weekly numbers of deaths and the corresponding prediction intervals for Vienna and the other Austrian provinces since 2007. Our analysis underlines the importance of comparing time series of COVID-19-related excess deaths at the sub-national level in order to highlight within-country heterogeneities.

Extended generator and associated martingales for M/G/1 retrial queue with classical retrial policy and general retrial times

A retrial queue with classical retrial policy, where each blocked customer in the orbit retries for service, and general retrial times is modeled by a piecewise deterministic Markov process (PDMP). From the extended generator of the PDMP of the retrial queue, we derive the associated martingales. These results are used to derive the conditional expected number of customers in the orbit in the transient regime.

Counting Non-Convex 5-Holes in a Planar Point Set

Let S be a set of n points in the general position, that is, no three points in S are collinear. A simple k-gon with all corners in S such that its interior avoids any point of S is called a k-hole. In this paper, we present the first algorithm that counts the number of non-convex 5-holes in S. To our best knowledge, prior to this work there was no known algorithm in the literature except a trivial brute force algorithm. Our algorithm runs in time O(T+Q), where T denotes the number of 3-holes, or empty triangles, in S and Q that denotes the number of non-convex 4-holes in S. Note that T+Q ranges from Ω(n2) to O(n3), while its expected number is Θ(n2logn) when the points in S are chosen uniformly and independently at random from a convex and bounded body in the plane.

Potential application of Rapid Antigen Diagnostic Tests for the detection of infectious individuals attending mass gatherings: a simulation study

Rapid Antigen Diagnostic Tests (RADTs) for the detection of SARS-CoV-2 offer advantages in that they are cheaper and faster than currently used PCR tests but have reduced sensitivity and specificity. One potential application of RADTs is to facilitate gatherings of individuals, through testing of attendees at the point of, or immediately prior to entry at a venue. Understanding the baseline risk in the tested population is of particular importance when evaluating the utility of applying diagnostic tests for screening purposes. We used incidence data to estimate the prevalence of infectious individuals in the community at a particular time point and simulated mass gatherings by sampling from a series of age cohorts. Nine different illustrative scenarios were simulated, small (n=100), medium (n=1000) and large (n=10,000) gatherings each with 3 possible age constructs: mostly younger, mostly older or a gathering with equal numbers from each age cohort. For each scenario, we estimated the prevalence of infectious attendees, then simulated the likely number of positive and negative test results, the proportion of cases detected and the corresponding positive and negative predictive values, and the cost per case identified. Our findings suggest that for each detected individual on a given day, there are likely to be 13.8 additional infectious individuals also present in the community. Prevalence of infectious individuals at events was highest with mostly younger attendees (1.00%), followed by homogenous age gatherings (0.55%) and lowest with mostly older events (0.26%). For small events (100 attendees) the expected number of infectious attendees was less than 1 across all age constructs of attendees. For large events (10,000 attendees) the expected number of infectious attendees ranged from 26 (95% confidence intervals 12 to 45) for mostly older events, to almost 100 (95% confidence intervals 46 to 174) infectious attendees for mostly younger attendees. Given rapid changes in SARS-CoV-2 incidence over time, we developed an RShiny app to allow users to run updated simulations for specific events.

Consultations for clinical features of possible cancer and associated urgent referrals before and during the COVID-19 pandemic: an observational cohort study from English primary care

Background It remains unclear to what extent reductions in urgent referrals for suspected cancer during the COVID-19 pandemic were the result of fewer patients attending primary care compared to GPs referring fewer patients. Methods Cohort study including electronic health records data from 8,192,069 patients from 663 English practices. Weekly consultation rates, cumulative consultations and referrals were calculated for 28 clinical features from the NICE suspected cancer guidelines. Clinical feature consultation rate ratios (CRR) and urgent referral rate ratios (RRR) compared time periods in 2020 with 2019. Findings Consultations for cancer clinical features decreased by 24.19% (95% CI: 24.04–24.34%) between 2019 and 2020, particularly in the 6–12 weeks following the first national lockdown. Urgent referrals for clinical features decreased by 10.47% (95% CI: 9.82–11.12%) between 2019 and 2020. Overall, once patients consulted with primary care, GPs urgently referred a similar or greater proportion of patients compared to previous years. Conclusion Due to the significant fall in patients consulting with clinical features of cancer there was a lower than expected number of urgent referrals in 2020. Sustained efforts should be made throughout the pandemic to encourage the public to consult their GP with cancer clinical features.

Pattern Avoidance Over a Hypergraph

A classic result of Marcus and Tardos (previously known as the Stanley-Wilf conjecture) bounds from above the number of $n$-permutations ($\sigma \in S_n$) that do not contain a specific sub-permutation. In particular, it states that for any fixed permutation $\pi$, the number of $n$-permutations that avoid $\pi$ is at most exponential in $n$. In this paper, we generalize this result. We bound the number of avoidant $n$-permutations even if they only have to avoid $\pi$ at specific indices. We consider a $k$-uniform hypergraph $\Lambda$ on $n$ vertices and count the $n$-permutations that avoid $\pi$ at the indices corresponding to the edges of $\Lambda$. We analyze both the random and deterministic hypergraph cases. This problem was originally proposed by Asaf Ferber. When $\Lambda$ is a random hypergraph with edge density $\alpha$, we show that the expected number of $\Lambda$-avoiding $n$-permutations is bounded (both upper and lower) as $\exp(O(n))\alpha^{-\frac{n}{k-1}}$, using a supersaturation version of F\"{u}redi-Hajnal. In the deterministic case we show that, for $\Lambda$ containing many size $L$ cliques, the number of $\Lambda$-avoiding $n$-permutations is $O\left(\frac{n\log^{2+\epsilon}n}{L}\right)^n$, giving a nontrivial bound with $L$ polynomial in $n$. Our main tool in the analysis of this deterministic case is the new and revolutionary hypergraph containers method, developed in papers of Balogh-Morris-Samotij and Saxton-Thomason.

The Temporal-Spatial Distribution and Information-Diffusion-Based Risk Assessment of Forest Fires in China

As forest fires are becoming a recurrent and severe issue in China, their temporal-spatial information and risk assessment are crucial for forest fire prevention and reduction. Based on provincial-level forest fire data during 1998–2017, this study adopts principal component analysis, clustering analysis, and the information diffusion theory to estimate the temporal-spatial distribution and risk of forest fires in China. Viewed from temporality, China’s forest fires reveal a trend of increasing first and then decreasing. Viewed from spatiality, provinces characterized by high population density and high coverage density are seriously affected, while eastern coastal provinces with strong fire management capabilities or western provinces with a low forest coverage rate are slightly affected. Through the principal component analysis, Hunan (1.33), Guizhou (0.74), Guangxi (0.51), Heilongjiang (0.48), and Zhejiang (0.46) are found to rank in the top five for the severity of forest fires. Further, Hunan (1089), Guizhou (659), and Guanxi (416) are the top three in the expected number of general forest fires, Fujian (4.70), Inner Mongolia (4.60), and Heilongjiang (3.73) are the top three in the expected number of large forest fires, and Heilongjiang (59,290), Inner Mongolia (20,665), and Hunan (5816) are the top three in the expected area of the burnt forest.