Learned behavioral avoidance can alter outbreak dynamics in a model for waterborne infectious diseases

Many animals show avoidance behavior in response to disease. For instance, in some species of frogs, individuals that survive infection of the fungal disease chytridiomycosis may learn to avoid areas where the pathogen is present. As chytridiomycosis has caused substantial declines in many amphibian populations worldwide, it is a highly relevant example for studying these behavioral dynamics. Here we develop compartmental ODE models to study the epidemiological consequences of avoidance behavior of animals in response to waterborne infectious diseases. Individuals with avoidance behavior are less likely to become infected, but avoidance may also entail increased risk of mortality. We compare the outbreak dynamics with avoidance behavior that is innate (present from birth) or learned (gained after surviving infection). We also consider how management to induce learned avoidance might affect the resulting dynamics. Using methods from dynamical systems theory, we calculate the basic reproduction number [Formula: see text] for each model, analyze equilibrium stability of the systems, and perform a detailed bifurcation analysis. We show that disease persistence when [Formula: see text] is possible with learned avoidance, but not with innate avoidance. Our results imply that management to induce behavioral avoidance can actually cause such a scenario, but it is also less likely to occur for high-mortality diseases (e.g., chytridiomycosis). Furthermore, the learned avoidance model demonstrates a variety of codimension-1 and -2 bifurcations not found in the innate avoidance model. Simulations with parameters based on chytridiomycosis are used to demonstrate these features and compare the outcomes with innate, learned, and no avoidance behavior.