早期跨洋航行的动力学：船员健康与生存的资源耦合模型
The dynamics of early transoceanic voyages: A resource-coupled model of crew health and survival
- Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出资源耦合的舱室模型，揭示早期跨洋航行中补给限制如何影响船员健康与操作能力，并引入临界补给时间，为历史过程提供定量视角。
AI中文摘要：
大航海时代的伟大跨洋航行给船员带来了严重的人员代价。漫长的航行时间、不断恶化的卫生条件以及有限的食物和淡水供应，使得疾病、疲惫和死亡成为海上扩张的核心特征。我们提出了一个最小化的舱室模型，将航行本身描述为一个耦合船员健康与资源消耗的动力系统。人群被分为健康者、患病者和死亡者，同时一个额外的变量代表船上补给的有效水平。疾病发生率非线性地依赖于资源的可用性，捕捉了与食物、淡水和卫生条件恶化相关的日益增加的健康风险。耦合的常微分方程在与有限时长航行相关的瞬态区域中进行分析。该模型并非重建特定的历史探险，而是识别出将补给、健康恶化、死亡率和航行时间联系起来的通用机制。数值结果表明，即使总体生存率保持相对较高，资源限制也能显著减少船员的健康和可操作部分，揭示了人口学意义上的生存与操作可行性之间的区别。增加初始补给会延迟患病者数量与健康者数量相等的交叉点，并延长船员保持主要可操作的时间段。我们还引入了一个临界补给时间，定义为资源达到预定压力阈值所需的时间，并发现其与初始资源缓冲大致呈线性关系。该框架为早期跨洋航行的内部动态提供了定量视角，并说明了动力系统方法如何有助于研究历史过程。
英文摘要：
The great transoceanic voyages of the Age of Discovery imposed severe human costs on their crews. Long travel durations, deteriorating sanitary conditions, and finite food and water supplies made disease, exhaustion, and mortality central features of maritime expansion. We propose a minimal compartmental model describing the voyage itself as a dynamical system coupling crew health and resource depletion. The population is divided into healthy, ill, and dead individuals, while an additional variable represents the effective level of provisions on board. Illness incidence depends nonlinearly on resource availability, capturing the increasing health risk associated with deteriorating food, water, and sanitary conditions. The coupled ordinary differential equations are analyzed in the transient regime relevant to finite-duration voyages. Rather than reconstructing specific historical expeditions, the model identifies generic mechanisms linking provisioning, health deterioration, mortality, and voyage duration. Numerical results show that resource limitations can substantially reduce the healthy and operational fraction of the crew even when overall survival remains relatively high, revealing a distinction between demographic survival and operational viability. Increasing initial provisioning delays the crossover at which ill individuals become as numerous as healthy individuals and extends the period over which the crew remains predominantly operational. We also introduce a critical provisioning time, defined as the time required for resources to reach a prescribed stress threshold, and find an approximately linear dependence on the initial resource buffer. The framework provides a quantitative perspective on the internal dynamics of early transoceanic navigation and illustrates how dynamical-systems approaches can contribute to the study of historical processes.
