At the moment we have more than 177 million cases and 3.8 million deaths (as of June 2021) around the world and vaccination represents the only hope to control the pandemic. Imperfections in planning vaccine acquisition and difficulties in implementing distribution among the population, however, have hampered the control of the virus so far. We propose a new mathematical model to estimate the impact of vaccination delay against the 2019 coronavirus disease (COVID-19) on the number of cases and deaths due to the disease in Brazil. We apply the model to Brazil as a whole and to the State of Sao Paulo, the most affected by COVID-19 in Brazil. We simulated the model for the populations of the State of Sao Paulo and Brazil as a whole, varying the scenarios related to vaccine efficacy and compliance from the populations. The model projects that, in the absence of vaccination, almost 170 thousand deaths and more than 350 thousand deaths will occur by the end of 2021 for Sao Paulo and Brazil, respectively. If in contrast, Sao Paulo and Brazil had enough vaccine supply and so started a vaccination campaign in January with the maximum vaccination rate, compliance and efficacy, they could have averted more than 112 thousand deaths and 127 thousand deaths, respectively. In addition, for each month of delay the number of deaths increases monotonically in a logarithmic fashion, for both the State of Sao Paulo and Brazil as a whole. Our model shows that the current delay in the vaccination schedules that is observed in many countries has serious consequences in terms of mortality by the disease and should serve as an alert to health authorities to speed the process up such that the highest number of people to be immunized is reached in the shortest period of time.

中文翻译：

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假设无限疫苗供应，模拟延迟接种 SARS-CoV-2 疫苗的影响

目前，全球有超过 1.77 亿例病例和 380 万例死亡（截至 2021 年 6 月），疫苗接种是控制大流行的唯一希望。然而，迄今为止，疫苗获取计划的不完善和人群分发的困难阻碍了病毒的控制。我们提出了一个新的数学模型来估计针对 2019 年冠状病毒病 (COVID-19) 的疫苗接种延迟对巴西该病病例数和死亡人数的影响。我们将该模型应用于整个巴西和巴西受 COVID-19 影响最严重的圣保罗州。我们模拟了整个圣保罗州和巴西人口的模型，改变了与疫苗效力和人口依从性相关的情景。该模型预测，在没有疫苗接种的情况下，到 2021 年底，圣保罗和巴西将分别有近 17 万人死亡和 35 万人死亡。相比之下，如果圣保罗和巴西有足够的疫苗供应，并因此在 1 月份以最高的疫苗接种率、依从性和有效性开始疫苗接种运动，它们可以分别避免超过 11.2 万例死亡和 12.7 万例死亡。此外，对于圣保罗州和巴西整体而言，每延迟一个月，死亡人数以对数方式单调增加。