Research on Mathematical Modeling of Infectious Disease Spread on Cruise Ships

Cruise ships, characterized by high density, enclosed environments and shared facilities, have become amplifiers for infectious disease outbreaks; however, predicting transmission in such settings remains challenging due to small initial case numbers. In this study, a mathematical modeling framework—including compartmental, small-world (SW), and scale-free (SF) network models—was developed to analyze the dynamics of hantavirus and norovirus transmission on recent cruise ship outbreaks. The results show that when the initial number of exposed or infected individuals is extremely small (e.g., 1–2 persons), disease spread is dominated by stochasticity, causing substantial variation between individual simulations and mean model predictions. Notably, SF networks exhibited lower transmission risk under these conditions, contradicting the theoretical expectation that when the population is large, SF networks facilitate the spread of disease. The compartmental model, while consistent with average simulation outcomes, failed to reliably predict any single outbreak event. In conclusion, for closed environments such as cruise ships with very few initial cases, stochastic variability is essential, and single-outbreak outcomes should be understood as highly contingent rather than deterministically predictable.