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Antiviral treatments for early intervention in patients with mild-to-moderate COVID-19 are needed as a complement to vaccination. We sought to estimate the impact on COVID-19 cases, deaths, and direct healthcare costs over 12 months following introduction of a novel, antiviral treatment, RD-X19, a light-based, at-home intervention designed for the treatment of mild-to-moderate COVID-19 infection. A time-dependent, state transition (semi-Markov) cohort model was developed to simulate infection progression in individuals with COVID-19 in 3 US states with varying levels of vaccine uptake (Alabama, North Carolina, and Massachusetts) and at the national level between 1 June 2020 and 31 May 2021. The hypothetical cohort of patients entering the model progressed through subsequent health states after infection. Costs were assigned to each health state. Number of infections/vaccinations per day were incorporated into the model. Simulations were run to estimate outcomes (cases by severity, deaths, and direct healthcare costs) at various levels of adoption of RD-X19 (5%, 10%, 25%) in eligible infected individuals at the state and national levels and across three levels of clinical benefit based on the results from an early feasibility study of RD-X19. The clinical benefit reflects a decline in the duration of symptomatic disease by 1.2, 2.4 (base case), and 3.6 days. In the base case analysis with 10% adoption, simulated infections/deaths/direct healthcare costs were reduced by 10,059/275/$69 million in Alabama, 21,092/545/$135 million in North Carolina, and 16,670/415/$102 million in Massachusetts over 12 months. At the national level, 10% adoption reduced total infections/deaths/direct healthcare costs by 686,722/17,748/$4.41 billion. At-home, antiviral treatment with RD-X19 or other interventions with similar efficacy that decrease both symptomatic days and transmission probabilities can be used in concert with vaccines to reduce COVID-19 cases, deaths, and direct healthcare costs.

The authors show how to determine the group generated by the ratios $(an+b)/(An+B)$ through its dual.

The purpose of the study was to assess the use of curative therapies for hepatocellular carcinoma (HCC) in the population. HCC treatment patterns were examined in Surveillance, Epidemiology, and End Results (SEER) 18 registries (28% of U.S.). Joinpoint regression analyses were performed to assess 2000-2010 incidence trends by tumor size, count, and receipt of potentially curative treatments (transplantation, resection, and ablation). SEER-Medicare data enabled evaluation of treatment patterns including receipt of sorafenib or transarterial chemoembolization (TACE) by HCC-associated comorbidities. Diagnoses of tumors≤5.0 cm in diameter significantly increased during 2000-2010, surpassing diagnosis of larger tumors. Overall, 23% of cases received potentially curative treatment. Joinpoint models indicated incidence rates of treatment with curative intent increased 17.6% per year during 2000-2005, then declined by -2.9% per year during 2005-2010 (P0.001). Among HCC cases with a single tumor≤5.0 cm and no extension beyond the liver, use of ablative therapy significantly increased during 2000-2010. Use of invasive surgery for single tumors, regardless of size, significantly increased during the initial years of the decade, then plateaued. The group most likely to receive curative treatment in the SEER-Medicare cases was patients with one, small tumor confined to the liver (657 of 1,597 cases, 41%), with no difference in treatment by hepatic comorbidity status (P=0.24). A higher proportion of cases with reported liver-associated comorbidities were, however, diagnosed with tumors≤5.0 cm in diameter (1,745 0f 2,464, 71%) compared to patients with no reported comorbidities (996 of 2,596, 38%, P0.001).Although more HCC patients were diagnosed with early disease over time, the use of curative treatments in this patient group has recently plateaued. Efforts to identify and treat more eligible candidates for curative therapy could be beneficial.

This is the first of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression and to the Fourier coefficients of automorphic cusp forms.

This is the second of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression and to the Fourier coefficients of automorphic cusp forms.

An inequality of Large Sieve type, efficacious in the analytic treatment of Euler products, is obtained., 3 pages

A method of estimating sums of multiplicative functions braided with Dirichlet characters is demonstrated, leading to a taxonomy of the characters for which such sums are large., Comment: 9 pages