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Accurate estimates of infection prevalence and seroprevalence are essential for evaluating and informing public health responses and vaccination coverage needed to address the ongoing spread of COVID-19 in each United States (U.S.) state. However, reliable, timely data based on representative population sampling are unavailable, and reported case and test positivity rates are highly biased. A simple data-driven Bayesian semi-empirical modeling framework was developed and used to evaluate state-level prevalence and seroprevalence of COVID-19 using daily reported cases and test positivity ratios. The model was calibrated to and validated using published state-wide seroprevalence data, and further compared against two independent data-driven mathematical models. The prevalence of undiagnosed COVID-19 infections is found to be well-approximated by a geometrically weighted average of the positivity rate and the reported case rate. Our model accurately fits state-level seroprevalence data from across the U.S. Prevalence estimates of our semi-empirical model compare favorably to those from two data-driven epidemiological models. As of December 31, 2020, we estimate nation-wide a prevalence of 1.4% [Credible Interval (CrI): 1.0%-1.9%] and a seroprevalence of 13.2% [CrI: 12.3%-14.2%], with state-level prevalence ranging from 0.2% [CrI: 0.1%-0.3%] in Hawaii to 2.8% [CrI: 1.8%-4.1%] in Tennessee, and seroprevalence from 1.5% [CrI: 1.2%-2.0%] in Vermont to 23% [CrI: 20%-28%] in New York. Cumulatively, reported cases correspond to only one third of actual infections. The use of this simple and easy-to-communicate approach to estimating COVID-19 prevalence and seroprevalence will improve the ability to make public health decisions that effectively respond to the ongoing COVID-19 pandemic. 

Disease epidemic outbreaks on human metapopulation networks are often driven by a small number of superspreader nodes, which are primarily responsible for spreading the disease throughout the network. Superspreader nodes typically are characterized either by their locations within the network, by their degree of connectivity and centrality, or by their habitat suitability for the disease, described by their reproduction number ( R ). Here we introduce a model that considers simultaneously the effects of network properties and R on superspreaders, as opposed to previous research which considered each factor separately. This type of model is applicable to diseases for which habitat suitability varies by climate or land cover, and for direct transmitted diseases for which population density and mitigation practices influences R . We present analytical models that quantify the superspreader capacity of a population node by two measures: probability-dependent superspreader capacity, the expected number of neighboring nodes to which the node in consideration will randomly spread the disease per epidemic generation, and time-dependent superspreader capacity, the rate at which the node spreads the disease to each of its neighbors. We validate our analytical models with a Monte Carlo analysis of repeated stochastic Susceptible-Infected-Recovered (SIR) simulations on randomly generated human population networks, and we use a random forest statistical model to relate superspreader risk to connectivity, R , centrality, clustering, and diffusion. We demonstrate that either degree of connectivity or R above a certain threshold are sufficient conditions for a node to have a moderate superspreader risk factor, but both are necessary for a node to have a high-risk factor. The statistical model presented in this article can be used to predict the location of superspreader events in future epidemics, and to predict the effectiveness of mitigation strategies that seek to reduce the value of R , alter host movements, or both.