The Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model is one of the standard models of disease spreading. Here we analyse an extended SEIR model that accounts for asymptomatic carriers, believed to play an important role in COVID-19 transmission. For this model we derive a number of analytic results for important quantities such as the peak number of infections, the time taken to reach the peak and the size of the final affected population. We also propose an accurate way of specifying initial conditions for the numerics (from insufficient data) using the fact that the early time exponential growth is well-described by the dominant eigenvector of the linearized equations. Secondly we explore the effect of different intervention strategies such as social distancing (SD) and testing-quarantining (TQ). The two intervention strategies (SD and TQ) try to reduce the disease reproductive number, $R_0,$ to a target value $R_0^{\text{target}}<1,$ but in distinct ways, which we implement in our model equations. We find that for the same $R_0^{\text{target}}<1,$ TQ is more efficient in controlling the pandemic than SD. However, for TQ to be effective, it has to be based on contact tracing and our study quantifies the required ratio of tests-per-day to the number of new cases-per-day. Our analysis shows that the largest eigenvalue of the linearised dynamics provides a simple understanding of the disease progression, both pre- and post- intervention, and explains observed data for many countries. We apply our results to the COVID data for India to obtain heuristic projections for the course of the pandemic, and note that the predictions strongly depend on the assumed fraction of asymptomatic carriers.

易感-暴露-感染-恢复 (SEIR) 流行病学模型是疾病传播的标准模型之一。在这里，我们分析了一个扩展的 SEIR 模型，该模型考虑了无症状携带者，据信这些携带者在 COVID-19 传播中起着重要作用。对于这个模型，我们得出了一些重要数量的分析结果，例如感染的峰值数量、达到峰值所需的时间以及最终受影响的人口规模。我们还提出了一种准确的方法来指定数值的初始条件（来自不足的数据），利用早期指数增长由线性化方程的主要特征向量很好地描述的事实。其次，我们探讨了不同干预策略的效果，例如社交距离 (SD) 和测试隔离 (TQ)。$R_0,$到一个目标值$R_0^{\text{目标}}<\mathrm{1个},$但以不同的方式，我们在我们的模型方程中实现。我们发现对于相同的$R_0^{\text{目标}}<\mathrm{1个},$TQ 在控制大流行方面比 SD 更有效。然而，要使 TQ 有效，它必须基于接触者追踪，并且我们的研究量化了每天测试与每天新病例数所需的比率。我们的分析表明，线性化动力学的最大特征值提供了对干预前和干预后疾病进展的简单理解，并解释了许多国家的观察数据。我们将我们的结果应用于印度的 COVID 数据，以获得对大流行过程的启发式预测，并注意到预测在很大程度上取决于无症状携带者的假定比例。