The ongoing coronavirus disease 2019 (COVID-19) pandemic poses a major threat to the worldwide health care. In this context, epidemic modelling is an integral part of containment strategies. Compartmental models are typically used for this purpose. Analytical solutions of the two distinct but connected Susceptible-Infectious-Recovered-Deceased (SIRD) and Susceptible-Infectious-Quarantine-Recovered (SIQR) models are presented in this study. Furthermore, the behaviour at the start of a disease outbreak is derived. This analysis shows that a combination of transmission, recovery and isolation rates dominates the behaviour at the start of an epidemic. In addition, the loss occurring due to quarantine and lockdown measures is investigated, where it can be observed that quarantine procedures lead to a smaller loss in comparison with lockdown regulations. Within this framework, optimized strategies that lead to a constant epidemic peak or a minimized loss are presented.

持续的 2019 年冠状病毒病 (COVID-19) 大流行对全球医疗保健构成重大威胁。在这种情况下，流行病建模是遏制策略的一个组成部分。隔间模型通常用于此目的。本研究介绍了两种不同但相互关联的易感感染康复者 (SIRD) 和易感感染隔离恢复 (SIQR) 模型的分析解决方案。此外，还得出疾病爆发开始时的行为。该分析表明，传播、恢复和隔离率的组合主导了流行病开始时的行为。此外，对隔离和封锁措施造成的损失进行了调查，可以观察到，与封锁规定相比，隔离程序导致的损失较小。