Complex dynamics induced by delayed adaptive behavior during epidemics

Ronan F. Arthur; James H. Jones; Matthew H. Bonds; Marcus W. Feldman

Our model makes a number of simplifying assumptions. We assume, for example, that all individuals in the population respond in the same fashion. We assume that the individuals choose their contact rates according to an optimized utility function, which is homogeneous across all individuals in the population. Finally, we assume that the utility function is symmetric around the optimal number of contacts so that increasing or decreasing contacts above or below the target contact rate respectfully yield the same reduction in utility. These assumptions allowed us to create the simplest possible model that includes adaptive behavior and time delay. In Holling's heuristic distinction in ecology between tactical models, models built to be parameterized and predictive, and strategic models, which aim to be as simple as possible to highlight phenomenelogical generalities, this is a strategic model [39] .