The presence of a large number of infected individuals with few or no symptoms is an important epidemiological difficulty and the main mathematical feature of COVID-19. The A-SIR model, i.e. a SIR (Susceptible–Infected–Removed) model with a compartment for infected individuals with no symptoms or few symptoms was proposed by Gaeta (2020). In this paper we investigate a slightly generalized version of the same model and propose a scheme for fitting the parameters of the model to real data using the time series only of the deceased individuals. The scheme is applied to the concrete cases of Lombardy, Italy and São Paulo state, Brazil, showing different aspects of the epidemic. In both cases we see strong evidence that the adoption of social distancing measures contributed to a slower increase in the number of deceased individuals when compared to the baseline of no reduction in the infection rate. Both for Lombardy and São Paulo we show that we may have good fits to the data up to the present, but with very large differences in the future behavior. The reasons behind such disparate outcomes are the uncertainty on the value of a key parameter, the probability that an infected individual is fully symptomatic, and on the intensity of the social distancing measures adopted. This conclusion enforces the necessity of trying to determine the real number of infected individuals in a population, symptomatic or asymptomatic.

存在大量症状很少或没有症状的感染者是一个重要的流行病学难题，也是 COVID-19 的主要数学特征。Gaeta (2020) 提出了 A-SIR 模型，即 SIR（易感-感染-去除）模型，其中包含用于无症状或很少症状的感染个体的隔室。在本文中，我们研究了同一模型的稍微通用的版本，并提出了一种仅使用已故个体的时间序列将模型参数拟合到真实数据的方案。该方案适用于意大利伦巴第和巴西圣保罗州的具体案例，展示了疫情的不同方面。在这两种情况下，我们都看到强有力的证据表明，与感染率没有降低的基线相比，采取社会疏远措施导致死亡人数增加较慢。对于伦巴第和圣保罗，我们表明我们可能对目前的数据有很好的拟合，但在未来的行为上有很大差异。这种不同结果背后的原因是关键参数值的不确定性、受感染者完全出现症状的可能性以及所采取的社会疏远措施的强度。这一结论强化了尝试确定有症状或无症状人群中受感染个体的实际数量的必要性。对于伦巴第和圣保罗，我们表明我们可能对目前的数据有很好的拟合，但在未来的行为上有很大差异。这种不同结果背后的原因是关键参数值的不确定性、受感染者完全出现症状的可能性以及所采取的社会疏远措施的强度。这一结论强化了尝试确定有症状或无症状人群中受感染个体的实际数量的必要性。对于伦巴第和圣保罗，我们表明我们可能对目前的数据有很好的拟合，但在未来的行为上有很大差异。这种不同结果背后的原因是关键参数值的不确定性、受感染者完全出现症状的可能性以及所采取的社会疏远措施的强度。这一结论强化了尝试确定有症状或无症状人群中受感染个体的实际数量的必要性。