The dynamics of early transoceanic voyages: A resource-coupled model of crew health and survival

The great transoceanic voyages of the Age of Discovery imposed severe human costs on the crews that sustained them. Long travel durations, deteriorating sanitary conditions and finite food and water supplies created an environment in which disease, exhaustion and mortality became central features of maritime expansion. Despite extensive historical documentation of these hardships, quantitative approaches rarely describe the voyage itself as a dynamical system coupling human health and resource depletion. In this work, we propose a minimal compartmental model for crew dynamics during long-distance oceanic expeditions. The population is divided into healthy, ill and dead individuals, while an additional dynamical variable represents the effective level of provisions on board. Disease incidence depends nonlinearly on resource availability, capturing the increasing health risk associated with deteriorating food, water and sanitary conditions. The resulting system of coupled ordinary differential equations is analyzed in the transient regime relevant to finite-duration voyages. Rather than reconstructing specific historical expeditions, the model aims to identify generic mechanisms governing the interplay between provisioning, health deterioration, mortality, and travel duration. Numerical results across a broad range of voyage durations and initial provisioning levels show that resource limitations may substantially reduce the healthy and operational fraction of the crew even when the overall survival fraction remains relatively high, revealing a clear distinction between demographic survival and operational viability. Increasing the initial provisioning level 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 further introduce a critical provisioning time, defined as the time required for resources to reach a prescribed stress threshold, and obtain an approximately linear dependence on the initial resource buffer. The framework provides a simple quantitative perspective on the internal dynamics of early transoceanic navigation and illustrates how dynamical-systems approaches can contribute to the study of historical processes.