In this paper, we study and simulate the effect of individual social responses, as a collective factor, on the epidemic spreading processes. We formally define the problem based on the traditional [Formula: see text] and [Formula: see text] compartmental models considering the time-varying infection probability dependent on the social responses. In this study, models of generic and special case scenarios are developed. While in the generic case the effective parameter of behavioral response is demonstrated as one collective factor, in the special case the behavioral response is assumed as the combination of two collective factors: social cost and transfer rate of social awareness. With social cost, we refer to the costs incurred by a certain population to prevent or mitigate an epidemic. With transfer rate of social awareness, we describe the averaged rate of received information and knowledge regarding a disease that individuals hold and make use to avoid negative consequences. We show that, while in both [Formula: see text] and [Formula: see text] models the density of infected agents grows exponentially during the initial time steps, the inclusion of our models of social responses, either generic or special one, leads to mitigation of the spreading. As a result of both generic and special cases, the density of infected agents in the stationary state and the maximum number of infected agents decrease according to power-law functions for different values of collective factors. In the special case results, we also witnessed significant changes in the slope of decreasing trends of stationary density of states happening for a critical value of transfer rate of social awareness, approximately at about the inverse of the time interval of transmission rate update. With this result, we point out that increasing the transfer rate of social awareness to about this critical point outperforms any slight increase in social cost in reducing the number of infected agents.

中文翻译：

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由于社会反应，具有时变传播率的无标度网络上的流行病传播现象

在本文中，我们研究并模拟了作为集体因素的个体社会反应对流行病传播过程的影响。我们基于传统的 [公式：见文本] 和 [公式：见文本] 分区模型正式定义问题，考虑了依赖于社会反应的时变感染概率。在这项研究中，开发了通用和特殊情况的模型。在一般情况下，行为反应的有效参数被证明为一个集体因素，而在特殊情况下，行为反应被假定为两个集体因素的组合：社会成本和社会意识的转移率。社会成本是指一定人群为预防或减轻流行病而发生的成本。随着社会意识的转移率，我们描述了个人为避免负面后果而持有和使用的有关疾病的信息和知识的平均接收率。我们表明，虽然在 [公式：参见文本] 和 [公式：参见文本] 模型中，受感染代理的密度在初始时间步长期间呈指数增长，但包含我们的社会反应模型，无论是通用的还是特殊的，都会导致以减缓传播。由于一般情况和特殊情况，静止状态下感染代理的密度和感染代理的最大数量根据集体因子的不同值的幂律函数降低。在特殊情况的结果中，我们还目睹了状态密度下降趋势的斜率的显着变化，这对于社会意识传递率的临界值发生了变化，大约与传递率更新时间间隔的倒数有关。有了这个结果，我们指出，将社会意识的转移率提高到这个临界点左右，在减少受感染的代理数量方面优于社会成本的任何轻微增加。