title: Pools versus Queues: The Variable Dynamics of Stochastic "Steady States".
abstract: Mathematical models in ecology and epidemiology often consider populations "at equilibrium", where in-flows, such as births, equal out-flows, such as death. For stochastic models, what is meant by equilibrium is less clear--should the population size be fixed or growing and shrinking with equal probability? Two different mechanisms to implement a stochastic steady state are considered. Under these mechanisms, both a predator-prey model and an epidemic model have vastly different outcomes, including the median population values for both predators and prey and the median levels of infection within a hospital (P < 0.001 for all comparisons). These results suggest that the question of how a stochastic steady state is modeled, and what it implies for the dynamics of the system, should be carefully considered.
authors.affiliation: Network Dynamics and Simulation Science Laboratory, Virginia Bioinformatics Institute Virginia Tech, Blacksburg, Virginia, United States of America.
authors.forename: Eric T
authors.initials: ET
authors.lastname: Lofgren
mesh_terms: D003428:Cross Infection / Q000453:epidemiology / Q000209:etiology; D006801:Humans; D008962:Models, Theoretical; D011157:Population Dynamics; D013269:Stochastic Processes