Cascade: an epidemiological model to simulate disease spread and aggregation across multiple scales in a spatial hierarchy.

Disease spread occurs at several spatial scales, e.g., from field to field, plant to plant, and leaf to leaf. So far, epidemiological models have largely overlooked the multiscale nature of epidemics. Here, we propose a model that simulates disease spread across multiple scales in a nested hierarchy. The model is based on the central ideas of hierarchy theory, i.e., (i) the system is decomposed vertically into levels and horizontally into holons (elements at one level, which are complete systems when seen from the lower level), and (ii) higher levels are characterized by slower processes than lower levels. The model is individual-based, the individuals being the holons, which are either susceptible or infected. At each level, infections within one holon (i.e., infections between holons of the level below) occur independently from the other holons: infections between holons happen at the higher level. The self-similarity of the model structure and processes across all levels allows implementing the model with a simple recursive algorithm. The behavior of the model was studied using methods commonly applied to field data. Aggregation of the disease was characterized through the incidence-incidence relationship and the binomial power law, in order to study the effect of infectiousness at each level on disease aggregation. Sensitivity analyses showed that disease incidences at all levels were influenced by the infectiousness at any level, but infectiousness at higher levels had more effect than infectiousness at lower levels. It was also shown that increasing the probability of infection at a given level increased aggregation at higher level(s) and decreased aggregation at lower level(s). The results were consistent between incidence-incidence relationship and power law analysis, but the incidence-incidence relationship was more sensitive in detecting the differences in aggregation between treatments.