Abstract

Based on a toy model for a trivial socioeconomic system, we demonstrate that the activation-type mechanism of the epidemic-resource coupling can lead to the collapsing effect opposite to thermal explosion. We exploit a SIS-like (susceptible-infected-susceptible) model coupled with the dynamics of average economic resource for a group of active economic agents. The recovery rate of infected individuals is supposed to obey the Arrhenius-like law, resulting in a mutual negative feedback between the number of active agents and resource acquisition. The economic resource is associated with the average amount of money or income per agent and formally corresponds to the effective market temperature of agents, with their income distribution obeying the Boltzmann–Gibbs statistics. A characteristic level of resource consumption is associated with activation energy. We show that the phase portrait of the system features a collapse phase, in addition to the well-known disease-free and endemic phases. The epidemic intensified by the increasing resource deficit can ultimately drive the system to a collapse at nonzero activation energy because of limited resource. We briefly discuss several collapse mitigation strategies involving either financial instruments like subsidies or social regulations like quarantine.

Graphic abstract

中文翻译：

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经济资源有限的系统中流行病导致崩溃的玩具模型

摘要

基于一个简单的社会经济系统的玩具模型，我们证明了流行病-资源耦合的激活型机制可以导致与热爆炸相反的崩溃效应。我们利用类似 SIS（易感-感染-易感）模型以及一组活跃经济主体的平均经济资源动态。被感染个体的恢复率应该服从类阿伦尼乌斯定律，导致活跃代理人的数量和资源获取之间相互负反馈。经济资源与每个代理人的平均金钱或收入相关，形式上对应于代理人的有效市场温度，其收入分布服从玻尔兹曼-吉布斯统计。资源消耗的特征水平与活化能相关。我们表明，除了众所周知的无病和地方病阶段外，系统的相图还具有崩溃阶段。由于资源有限，资源短缺加剧的流行病最终会导致系统在非零活化能下崩溃。我们简要讨论了几种缓解崩溃的策略，涉及补贴等金融工具或检疫等社会法规。

图形摘要