Modelling the spreading of the SARS-CoV-2 in presence of the lockdown and quarantine measures by a kinetic-type reactions approach.

IF 0.8 4区 数学 Q4 BIOLOGY Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2022-06-11 DOI:10.1093/imammb/dqab017
Giorgio Sonnino, Philippe Peeters, Pasquale Nardone
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引用次数: 4

Abstract

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.

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通过动力学型反应方法模拟在封锁和隔离措施下SARS-CoV-2的传播。
我们为新冠肺炎大流行的演变提出了一个现实的模型,该模型受封锁和隔离措施的影响,其中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导出了整个过程的动力学方程。更具体地说,封锁和隔离措施是由某种抑制剂反应模拟的,在这种反应中,易感和受感染的人可能会被困在不活跃的状态中。康复者的动态是通过统计只追溯到住院感染者的人数来获得的。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,其中酶分别与可用的病床、感染者的底物和康复者的产物有关。换言之,一切都发生在医院病床在医院恢复过程中起着催化剂的作用。当然,在我们的例子中,反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,新冠肺炎检测呈阳性的人的常微分方程(ODEs)简单地通过以下动力学方案$S+I\Rightarrow 2I$建模,其中$I\Rigightarrow R$或$I\Rightarrow D$,其中$S$、$I$、$R$和$D$分别表示易感、感染、康复和死亡的人。由此产生的动力学类型方程为基本反应步骤提供了ODE,描述了受封锁和隔离措施影响的感染者人数、先前住院的康复者总数以及死亡总数。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。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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