The Diffusion Process of Spanish Influenza Deaths in Japan: Mathematical Models Using the Gompertz and Logistic Curves

This chapter examines the diffusion process of deaths due to the Spanish influenza pandemic using mortality statistics from Japan. For this purpose, the study constructs four modified models, based on the Gompertz and logistic curves, that incorporate an initial effect and a winter effect. These models are then applied to the second wave of the Spanish influenza. In applying them, Japanese prefectures are classified into five types; the average monthly mortality rates are calculated for each type, and the calculated cumulative mortality rates are used as the models’ variables. The results of the model analysis can be summarized as follows: First, the winter effect appears to be stronger than the initial effect. Second, the Gompertz curve-based model tends to better fit region types with relatively high population density, while the logistic curve-based model tends to better fit the opposite types. Third, region types following the Gompertz curve typically have higher final cumulative mortality rates than those following the logistic curve. Since the high influenza mortality rate among the elderly is a significant issue in contemporary Japan, these results can be expected to contribute to improving that mortality rate and advancing gerontology.