The complexity associated with an epidemic defies any quantitatively reliable predictive theoretical scheme. Here, we pursue a generalized mathematical model and cellular automata simulations to study the dynamics of infectious diseases and apply it in the context of the COVID-19 spread. Our model is inspired by the theory of coupled chemical reactions to treat multiple parallel reaction pathways. We essentially ask the question: how hard could the time evolution toward the desired herd immunity (HI) be on the lives of people? We demonstrate that the answer to this question requires the study of two implicit functions, which are determined by several rate constants, which are time-dependent themselves. Implementation of different strategies to counter the spread of the disease requires a certain degree of a quantitative understanding of the time-dependence of the outcome. Here, we compartmentalize the susceptible population into two categories, (i) vulnerables and (ii) resilients (including asymptomatic carriers), and study the dynamical evolution of the disease progression. We obtain the relative fatality of these two sub-categories as a function of the percentages of the vulnerable and resilient population and the complex dependence on the rate of attainment of herd immunity. We attempt to study and quantify possible adverse effects of the progression rate of the epidemic on the recovery rates of vulnerables, in the course of attaining HI. We find the important result that slower attainment of the HI is relatively less fatal. However, slower progress toward HI could be complicated by many intervening factors.

中文翻译：

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传染病动力学的数学建模和细胞自动机模拟：在了解牛群免疫性方面的应用。

与流行病相关的复杂性无视任何在定量上可靠的预测理论方案。在这里，我们追求通用的数学模型和细胞自动机模拟，以研究传染病的动态并将其应用于COVID-19传播的情况。我们的模型受耦合化学反应理论的启发，该理论可以处理多个平行的反应途径。我们本质上是在问一个问题：朝着理想的群体免疫（HI）的时间演变对人们的生命有多困难？我们证明，这个问题的答案需要研究两个隐式函数，这两个隐函数由几个速率常数决定，它们本身与时间有关。采取不同策略来应对疾病的传播，需要对结果的时间依赖性有一定程度的定量了解。在这里，我们将易感人群分为两类，（i）脆弱人群和（ii）弹性人群（包括无症状携带者），并研究疾病进展的动态演变。我们获得了这两个子类别的相对死亡率，这是脆弱和具有韧性的人口所占百分比以及对获得牛群免疫率的复杂依赖性的函数。我们发现重要的结果是，较慢达到HI的致命性相对较小。但是，由于许多中间因素，向HI的缓慢进展可能会变得复杂。