There are multiple sources of data giving information about the number of SARS-CoV-2 infections in the population, but all have major drawbacks, including biases and delayed reporting. For example, the number of confirmed cases largely underestimates the number of infections, and deaths lag infections substantially, while test positivity rates tend to greatly overestimate prevalence. Representative random prevalence surveys, the only putatively unbiased source, are sparse in time and space, and the results can come with big delays. Reliable estimates of population prevalence are necessary for understanding the spread of the virus and the effectiveness of mitigation strategies. We develop a simple Bayesian framework to estimate viral prevalence by combining several of the main available data sources. It is based on a discrete-time Susceptible–Infected–Removed (SIR) model with time-varying reproductive parameter. Our model includes likelihood components that incorporate data on deaths due to the virus, confirmed cases, and the number of tests administered on each day. We anchor our inference with data from random-sample testing surveys in Indiana and Ohio. We use the results from these two states to calibrate the model on positive test counts and proceed to estimate the infection fatality rate and the number of new infections on each day in each state in the United States. We estimate the extent to which reported COVID cases have underestimated true infection counts, which was large, especially in the first months of the pandemic. We explore the implications of our results for progress toward herd immunity.

有多种数据来源可以提供有关人群中 SARS-CoV-2 感染数量的信息，但所有数据都存在重大缺陷，包括偏见和延迟报告。例如，确诊病例数很大程度上低估了感染人数，死亡人数大大滞后于感染人数，而检测阳性率往往大大高估了患病率。代表性随机流行率调查是唯一被认为无偏见的来源，但在时间和空间上都很稀疏，而且结果可能会出现很大的延迟。对人口患病率的可靠估计对于了解病毒的传播和缓解策略的有效性是必要的。我们开发了一个简单的贝叶斯框架，通过结合几个主要的可用数据源来估计病毒流行率。它基于具有随时间变化的繁殖参数的离散时间易感-感染-移除 (SIR) 模型。我们的模型包括可能性成分，其中包含病毒导致的死亡、确诊病例以及每天进行的检测数量的数据。我们根据印第安纳州和俄亥俄州随机样本测试调查的数据来进行推断。我们使用这两个州的结果来校准阳性检测计数模型，并继续估计美国每个州每天的感染死亡率和新增感染人数。我们估计报告的新冠病例在多大程度上低估了真实的感染人数，这一数字很大，尤其是在大流行的头几个月。我们探讨了我们的结果对群体免疫进展的影响。