We propose a realistic model for the evolution of the COVID-19 pandemic subject to the lockdown and quarantine measures, which takes into account the timedelay for recovery or death processes. The dynamic equations for the entire process are derived by adopting a kinetic-type reactions approach. More specifically, the lockdown and the quarantine measures are modelled by some kind of inhibitor reactions where susceptible and infected individuals can be trapped into inactive states. The dynamics for the recovered people is obtained by accounting people who are only traced back to hospitalized infected people. To get the evolution equation we take inspiration from the Michaelis Menten's enzyme-substrate reaction model (the so-called MM reaction) where the enzyme is associated to the available hospital beds, the substrate to the infected people, and the product to the recovered people, respectively. In other words, everything happens as if the hospitals beds act as a catalyzer in the hospital recovery process. Of course, in our case, the reverse MM reaction has no sense in our case and, consequently, the kinetic constant is equal to zero. Finally, the ordinary differential equations (ODEs) for people tested positive to COVID-19 is simply modelled by the following kinetic scheme $S+I\Rightarrow 2I$ with $I\Rightarrow R$ or $I\Rightarrow D$, with $S$, $I$, $R$ and $D$ denoting the compartments susceptible, infected, recovered and deceased people, respectively. The resulting kinetic-type equations provide the ODEs, for elementary reaction steps, describing the number of the infected people, the total number of the recovered people previously hospitalized, subject to the lockdown and the quarantine measure and the total number of deaths. The model foresees also the second wave of infection by coronavirus. The tests carried out on real data for Belgium, France and Germany confirmed the correctness of our model.

中文翻译：

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通过动力学型反应方法对封锁和隔离措施下 SARS-CoV-2 的传播进行建模。

我们提出了一个在封锁和隔离措施下的 COVID-19 大流行演变的现实模型，该模型考虑了恢复或死亡过程的时间延迟。采用动力学型反应方法推导了整个过程的动力学方程。更具体地说，封锁和隔离措施是以某种抑制剂反应为模型的，易感者和受感染者可能会陷入不活跃状态。康复者的动态是通过会计人员获得的，这些人员仅追溯到住院的感染者。为了得到进化方程，我们从 Michaelis Menten 的酶-底物反应模型（所谓的 MM 反应）中获得灵感，其中酶与可用的医院床位相关，底物与感染者相关，产物与康复者相关， 分别。换句话说，一切的发生就好像医院的病床在医院康复过程中充当了催化剂一样。当然，在我们的例子中，逆 MM 反应在我们的例子中没有意义，因此，动力学常数等于 0。最后，COVID-19 测试呈阳性的人的常微分方程 (ODE) 可以通过以下动力学方案 $S+I\Rightarrow 2I$ 和 $I\Rightarrow R$ 或 $I\Rightarrow D$ 简单建模，其中 $ S$、$I$、$R$ 和 $D$ 分别表示易感人群、感染人群、康复人群和死亡人群。由此产生的动力学方程提供了基本反应步骤的常微分方程，描述了感染人数、之前住院的康复者总数（受封锁和隔离措施影响）以及死亡总数。该模型还预测了冠状病毒的第二波感染。对比利时、法国和德国的真实数据进行的测试证实了我们模型的正确性。