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

Abstract

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.