论文标题
动力学理论和大流行的细胞自动机模拟：了解不同感染的时间模式
Dynamical Theory and Cellular Automata Simulations of Pandemic Spread: Understanding Different Temporal Patterns of Infections
论文作者
论文摘要
在这里，我们提出并实施了一个广义的数学模型，以找到传染病中人群的时间演变，并应用模型研究最近的Covid-19-19。我们的核心模型是对广泛使用的Kermack-Mckendrick（KM）模型的非本地概括，其中易感人群分为另外两个类别，即感染（I）和删除（R）。这是众所周知的SIR模型，在其中我们将S和I分为高风险类别。我们首先制定了一组非本地动力学方程，以在此分类下的不同种群分布的时间演变，以尝试描述传染病进展的一般情况。然后，我们通过传播方法来求解非线性耦合微分方程 - （i），以及（ii）更灵活，更广泛的蜂窝自动机（CA）模拟，该模拟提供了对广义非局部模型的粗粒描述。为了说明多种因素，例如在围栏前的作用，我们引入了一个依赖时间的速率，这对于在许多情况下观察到高原之前的突然峰值似乎至关重要（例如，像中国一样）。我们展示了这种广义方法如何使我们能够处理（i）扩散速率代理的时间依赖性，（ii）不同的人口密度，（iii）年龄比，（iv）隔离，（v）锁定和（vi）社会疏远。我们的研究使我们能够对几个外部参数的传播性质做出一定的预测，该参数被视为控制变量。该模型的分析清楚地表明，由于源自初始感染的分布的流行过程中的强大异质性，该理论必须在特征上是局部的，但同时又连接到了全球观点。
Here we propose and implement a generalized mathematical model to find the time evolution of population in infectious diseases and apply the model to study the recent COVID-19 pandemic. Our model at the core is a non-local generalization of the widely used Kermack-McKendrick(KM) model where the susceptible(S) population evolves into two other categories, namely infectives(I) and removed(R). This is the well-known SIR model in which we further divide both S and I into high and low risk categories. We first formulate a set of non-local dynamical equations for the time evolution of distinct population distributions under this categorization in an attempt to describe the general scenario of infectious disease progression. We then solve the non-linear coupled differential equations-(i) numerically by the method of propagation, and (ii) a more flexible and versatile cellular automata (CA) simulation which provides a coarse-grained description of the generalized non-local model. In order to account for multiple factors such as role of spreaders before containment, we introduce a time dependent rate which appears to be essential to explain the sudden spikes before the plateau observed in many cases (for example like China). We demonstrate how this generalized approach allows us to handle the effects of (i) time-dependence of the rate-constants of spread, (ii) different population density, (iii) the age ratio, (iv) quarantine, (v) lockdown, and (vi) social distancing. Our study allows us to make certain predictions regarding the nature of spread with respect to several external parameters, treated as control variables. Analysis of the model clearly shows that due to the strong heterogeneity in the epidemic process originating from the distribution of initial infectives, the theory must be local in character but at the same time connect to a global perspective.
