Resilience, tipping, and hydra effects in public health: emergent collective behavior in two agent-based models

Collective health behavior often demonstrates counter-intuitive dynamics, sometimes resisting interventions designed to produce change, or even producing effects that are in the opposite direction than intended by the intervention, e.g. lowering infectivity resulting in increased infections. At other times collective health behavior exhibits sudden large-scale change in response to small interventions or change in the environment, a phenomenon often called “tipping.” I hypothesize that these seemingly very different phenomena can all be explained by the same dynamic, a type of collective resilience.

I compared two simple agent-based models of interactions in networks: a public health behavior game, in which individuals decide whether or not to adopt protective behavior, and a microbial-level game, in which three different strains of bacteria attack each other. I examined the type of networks and other conditions that support a dynamic balance, and determined what changes of conditions will tip the balance.

Both models show lasting dynamic equilibrium and resilience, resulting from negative feedback that supports oscillating coexistence of diversity under a range of conditions. In the public health game, health protection is followed by free-riding defectors, followed by a rise in infection, in long-lasting cycles. In the microbial game, each of three strains takes turns dominating. In both games, the dynamic balance is tipped by lowering the level of local clustering, changing the level of benefit, or lowering infectivity or attack rate. Lowering infectivity has the surprising effect of increasing the numbers of infected individuals. We see parallel results in the microbial game of three bacterial strains, where lowering one strain’s attack rate (analogous to lowering infectivity) increases the numbers of the restrained attacker, a phenomenon captured by the phrase, “the enemy of my enemy is my friend.”

Collective behavior often shows a dynamic balance, resulting from negative feedback, supporting diversity and resisting change. Above certain threshold conditions, the dynamic balance is tipped towards uniformity of behavior. Under a certain range of conditions we see “hydra effects” in which interventions to lower attack rate or infectivity are self-defeating. Simple models of collective behavior can explain these seemingly disparate dynamics.