近年来，COVID-19疫情成为全球政府、科学界以及民众最为关注的突发公共卫生问题。在相关研究领域中，通过使用传染病模型对疫情进行解释以及参数预测成为数学与统计学专家关注的焦点。与历史上其他新发传染病相比，COVID-19的持续传播能力更加强大，尽管已经采取了大规模的防控措施和疫苗接种，其发展依旧不断变化且充满不确定性，给流行病学模型的构建与分析带来了空前的挑战。

本研究对分阶段传染病模型进行研究及应用，循序渐进地完成三种由数据驱动、基于传染病模型的建模设计。在第一部分中，针对疫情早期阶段，建立了一种包含无症状感染者和未报告有症状感染者的SAIUHR传染病模型。接着，根据所建立的模型提出了一种计算各种传染病学参数以及仓室初值变量（如报告率、传播率、动态病死率等）的方法。并基于典型国家的疫情数据对早期疫情进行拟合以及防控措施的量化分析。同时也凸显了早期阶段有效的防控措施对疫情发展的重要性。

第二部分研究重点对经历过大规模疫苗接种政策的国家进行长期疫情情况的分析，创新地使用不断更新的疫苗接种数据构建了SEAIUHR传染病模型，接着将模型与可能导致疾病传播的外在因素（疫苗效率、未报告率、社交距离措施）联系起来，给出了一种计算分段时变传播率的方法。并基于美国的疫苗数据以及累计确诊数据进行了长期疫情的实证研究，结果显示利用这种方法并结合流行病学数据，可以更清楚地了解流行病的传播规律，为后续的相关研究提供数据支持，同时也反映了不同防控措施以及疫苗效率对疫情控制效果的差异。

然而，随着疫情长时间的蔓延，多阶段的爆发使疫情曲线更加复杂，但世界不同地区的疫情发展趋势往往是相似的，即在初始阶段过后呈现多重流行波的增长模式。第三部分，构建了一个现象学模型，在不损失相关信息的情况下减少必要参数的数量，并对不同规模的流行波进行了深入探索，完成了对流行病学和统计学参数（传播率、初值变量、无症状感染病例曲线、未报告有症状感染病例曲线、日新增病例峰值）的完整推断，并使用Savitzky-Golay滤波器对不同阶段过渡处进行平滑处理从而帮助减少突变点对研究结果的影响。

综合来看，本文涵盖的三项研究对于不同阶段和不同对象的疫情展示了出色的解释以及预测能力。虽然使用的建模方法均不相同，但这三项研究以循序渐进的方式展开，通过不断地创新和改进，结合了多种统计以及数学方法，有效克服了以往研究的不足和局限。

In recent years, COVID-19 has become a public health concern for governments, research communities, and the public. Among relevant literature, employing epidemiological models for explanatory analysis and forecasting of epidemic trends is the focus for mathematicians and statisticians. Compared with other emerging infectious diseases in history, the sustained transmission capacity of COVID-19 is even stronger. Despite large-scale prevention and control measures and vaccination, its development is still constantly changing and full of uncertainty, which is substantially challenging for the construction and analysis of epidemiological models.

This study investigates and applies a phased infectious disease model, gradually completing three data-driven, infectious disease model-based modeling designs. In the first part of the research, a SAIUHR model, which describes the dynamic changes of susceptible, asymptomatic infectious, under-reported symptomatic infectious, hospitalized, and recovered individuals, was constructed for the early stages of the epidemic. Subsequently, a novel approach was proposed, based on the established model, to calculate the report rate, starting time, basic reproduction number, the initial conditions for the compartments, CFR, and DCFR. Based on epidemiological datasets of typical countries, fit the early epidemic and quantitatively analyze the prevention and control measures. At the same time, it also highlights the implications of taking proper restrictions and strong policies to deal with emerging and re-emerging infectious diseases from their spread in the early stage.

The second part of the research focuses on analyzing the long-term epidemic situation of countries that have experienced large-scale vaccination policies. This study fully utilized continuously updated real-time epidemiological data and proposed a SEAIUHR model incorporating asymptomatic and symptomatic infectiousness, reported and under-reported cases, inpatient and non-inpatient cases, and vaccine inoculation. This study proposed a novel approach based on the model to calculate the time-varying transmission rate with an under-report rate, vaccination efficiency, and relaxation of social distancing behavior. The proposed method was evaluated based on epidemiological data from the United States. The results suggest that using this approach to combine epidemiological data can provide a clearer understanding of the spread rule of the epidemic, offering data support for subsequent related research. This also highlights variations in the effectiveness of diverse prevention and control measures, as well as vaccine efficiency, in epidemic management.

However, with the prolonged spread of the epidemic, multi-stage outbreaks have made the epidemic curve more complex. The development trends of the epidemic in different regions of the world are often similar, showing a growth pattern of multiple epidemic waves after the initial stage. In the third part of the research, a phenomenological model was constructed to reduce the number of parameters without losing relevant information, and in-depth exploration was conducted on epidemic waves of different scales. Subsequently, the complete inference of epidemiological and statistical parameters, including the time-varying transmission rate, initial variables, asymptomatic infection case curve, under-reported symptomatic infection case curve, and daily peak of new cases, was completed. Furthermore, Savitzky-Golay filters are used to smooth transitions at different stages, helping to reduce the impact of change-point on research results.

Overall, the three studies presented in this study have demonstrated excellent explanatory and predictive abilities for epidemics at different stages and targets. Although different modeling methods were used, these three studies were conducted progressively, combining multiple statistical and mathematical methods through continuous innovation and improvement, effectively overcoming the shortcomings and limitations of previous research.