A Stochastic Cooperative Agent Model of Band-Pass Antibiotic Resistance*

The recently described phenomenon of band-pass antibiotic resistance occurs when bacteria exposed to a periodic environment of oscillating antibiotic concentration grow fastest at intermediate period lengths. Previously, it has been shown that such behavior can arise from a non-linearity in individual fitness as a function of the initial colony density, called the ``Allee effect,'' as well as a fixed-point catastrophe that depends very strongly on the antibiotic concentration. Here, we present a new agent-based, \textit{in silico} stochastic model of cooperative antibiotic resistance. This model attempts to capture the behavior of ``cooperative'' bacteria that, for example, expend resources to produce enzymes that break down $\beta $-lactam antibiotic molecules, but are subject to the problem of freeloading by non-secretors that benefit but do not contribute. Colony survival can be threatened when exposed to a periodic antibiotic challenge. By creating a simulation in which the bacteria are modeled as stochastic agents, the effect of antibiotic concentration, period of antibiotic oscillation, and degree of cooperativity can be evaluated.