The COVID-19 pandemic (SARS-CoV-2 virus) is the global crisis of our time. The absence of mass testing and the relevant presence of asymptomatic individuals causes the available data of the COVID-19 pandemic in Brazil to be largely under-reported regarding the number of infected individuals and deaths. We develop an adapted Susceptible-Infected-Recovered (SIR) model, which explicitly incorporates the under-reporting and the response of the population to public health policies (confinement measures, widespread use of masks, etc). Large amounts of uncertainty could provide misleading predictions of the COVID-19 spread. In this paper, we discuss the role of uncertainty in these model-based predictions, which is illustrated regarding three key aspects: (i) Assuming that the number of infected individuals is under-reported, we demonstrate anticipation regarding the infection peak. Furthermore, while a model with a single class of infected individuals yields forecasts with increased peaks, a model that considers both symptomatic and asymptomatic infected individuals suggests a decrease of the peak of symptomatic cases. (ii) Considering that the actual amount of deaths is larger than what is being registered, we demonstrate an increase of the mortality rates. (iii) When we consider generally under-reported data, we demonstrate how the transmission and recovery rate model parameters change qualitatively and quantitatively. We also investigate the “the uncertainty tripod”: under-reporting level in terms of cases, deaths, and the true mortality rate of the disease. We demonstrate that if two of these factors are known, the remainder can be inferred, as long as proportions are kept constant. The proposed approach allows one to determine the margins of uncertainty by assessments on the observed and true mortality rates.

COVID-19大流行（SARS-CoV-2病毒）是当今时代的全球危机。由于没有进行大规模检测，也没有相关的无症状个体，致使巴西关于COVID-19大流行的可用数据在被感染个体的数量和死亡方面的报道不足。我们开发了一种适应性传染病恢复（SIR）模型，该模型明确纳入了人口不足报告和民众对公共卫生政策（禁毒措施，口罩的广泛使用等）的反应。大量的不确定性可能会对COVID-19传播提供误导性的预测。在本文中，我们讨论了不确定性在这些基于模型的预测中的作用，并从三个关键方面对此进行了说明：（i）假设被感染个体的数量未得到充分报告，我们证明了有关感染高峰的预期。此外，虽然只有一类受感染个体的模型产生的预测峰值会增加，但同时考虑有症状和无症状的受感染个体的模型却表明有症状病例的峰值减少了。（ii）考虑到实际死亡人数大于所记录的死亡人数，我们证明了死亡率的增加。（iii）当我们考虑总体上报告不足的数据时，我们证明了传输率和恢复率模型参数如何定性和定量地变化。我们还调查了“不确定性三脚架”：在病例，死亡和疾病的真实死亡率方面的报告不足水平。我们证明，如果其中两个因素已知，则可以推断出其余因素，只要比例保持恒定即可。所提出的方法允许通过评估观察到的和真实的死亡率来确定不确定性的余量。