Math Biology Seminar: Gregory Kelly

Dynamic systems (SIR/compartmental models) have equilibriums that can be derived through algebraic techniques. The algebraic solutions rapidly reproduce results given by next generation matrix and center manifold theory, but contain additional information useful for understanding disease dynamics in the presence of hysteresis within communities.  Hysteresis is present in several West Nile virus models, leading to predictions of continued disease prevalence even when conditions would prevent an outbreak from occurring. The algebraic solutions offer a method to classify disparate WNv models into similarly behaving groups.