Université Libre de Bruxelles (ULB), Faculté de Sciences Bvd du Triomphe, Campus Plaine CP 231, 1050 Brussels, Belgium.
Math Med Biol. 2022 Jun 11;39(2):105-125. doi: 10.1093/imammb/dqab017.
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.
我们提出了一个现实的 COVID-19 大流行演变模型，该模型考虑了恢复或死亡过程的时滞，同时还考虑了封锁和检疫措施。采用动力学型反应方法推导出整个过程的动态方程。更具体地说，通过某种抑制剂反应来模拟封锁和检疫措施，使易感者和感染者可以被困在非活跃状态。通过考虑仅追溯到住院感染者的人来获得康复者的动态。为了得到演化方程，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联，底物与感染者相关联，产物与康复者相关联。换句话说，就好像医院床位在医院康复过程中充当了催化剂。当然，在我们的情况下，反向 MM 反应在我们的情况下没有意义，因此动力学常数等于零。最后，将 COVID-19 检测呈阳性的人的常微分方程（ODE）简单地建模为以下动力学方案$S+I\Rightarrow 2I$，其中$I\Rightarrow R$或$I\Rightarrow D$，其中$S$、$I$、$R$和$D$分别表示易感者、感染者、康复者和死亡者的隔室。产生的动力学型方程为基本反应步骤提供了 ODE，用于描述感染者数量、之前住院的康复者总数、封锁和检疫措施以及死亡总数。该模型还预测了冠状病毒的第二波感染。对比利时、法国和德国的实际数据进行的测试证实了我们模型的正确性。
