A Behavioral Multispread Epidemic Model

Graziani, C.

We introduce a class of epidemic models that represent multiple spread rates in terms of discrete behavior classes, rather than in terms of discrete compartments comprising individuals. The model is framed in terms of D behavior classes, each with its own spread rate. The population is represented as a density on the D-simplex, where each point is a D-vector f whose components sum to 1. Each component of f represents the fraction of time in which an individual spends engaging in the corresponding behavior. The evolution equation is an integro-differential equation on the D-simplex. The model is capable of describing the "superspreader" phenomenon in terms of behavior spread rates, as opposed to terms of individual infectivity. We show the existence of SIR-like separable solutions and discuss their stability. We explore the numeric properties of the model using a D=3 case featuring a "safe" behavior, a moderate-spread behavior, and a superspread behavior.