论文标题
建模SARS-COV2及其变体的传播。与真实数据的比较。必须满足的关系才能实现SARS-COV2感染的总回归
Modelling the Spread of SARS-CoV2 and its variants. Comparison with Real Data. Relations that have to be Satisfied to Achieve the Total Regression of the SARS-CoV2 Infection
论文作者
论文摘要
这项工作提供了有关确定性和随机模型的概述，我们以前提出了研究欧洲和美国冠状病毒病2019（COVID-19）的传播动力学。简而言之，我们描述了由锁定和隔离措施的封锁和隔离措施的现实确定性和随机模型，这些模型考虑了恢复或死亡过程的时间延迟。通过采用所谓的“动力学型反应方法”来得出整个过程的现实动态方程。锁定和隔离措施是由某种抑制剂反应建模的，在这些抑制剂反应中，易感和感染的个体可以“被困”到不活跃状态中。通过核算仅追溯到住院的感染者的人来获得恢复人的动态。为了模拟医院的作用，我们从Michaelis-Menten的酶 - 基底反应模型（所谓的“ MM反应”）中汲取灵感，其中“酶”与“可用的医院床”（分别与“感染者”的“可用医院床”相关联，分别与“恢复的人”相关。已适当评估了模型的统计特性，特别是相关的相关函数和概率密度函数。我们使用大量意大利，德国，法国，比利时和美国的一系列实验数据来验证我们的理论预测，我们还将意大利和比利时的数据与逻辑模型的理论预测进行了比较。我们发现，自Covid 19的开始以来，我们的预测与现实世界吻合，这与仅适用于大流行的第一天的物流模型相反。在工作的最后部分，我们可以找到应满足的（理论上的）关系，以获得病毒的消失。
This work provides an overview on deterministic and stochastic models that have previously been proposed by us to study the transmission dynamics of the Coronavirus Disease 2019 (COVID-19) in Europe and USA. Briefly, we describe realistic deterministic and stochastic models for the evolution of the COVID-19 pandemic, subject to the lockdown and quarantine measures, which take into account the time-delay for recovery or death processes. Realistic dynamic equations for the entire process have been derived by adopting the so-called "kinetic-type reactions approach". 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 hospitalised infected people. To model the role of the Hospitals 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. The statistical properties of the models, in particular the relevant correlation functions and the probability density functions, have duly been evaluated. We validate our theoretical predictions with a large series of experimental data for Italy, Germany, France, Belgium and United States, and we also compare data for Italy and Belgium with the theoretical predictions of the logistic model. We found that our predictions are in good agreement with the real world since the onset of COVID 19, contrary to the the logistics model that only applies in the first days of the pandemic. In the final part of the work, we can find the (theoretical) relationships that should be satisfied to obtain the disappearance of the virus.
