Speaker: Dr. Mustafa Erdem,
Department of Mathemetics and Statistics,
ASU

Title: Epidemics in Structured Populations with Isolation

Abstract: This work has been motivated by the evolutionary dynamics of infectious diseases. Hence, the goal of this research addresses some of the challenges posed by the transmission dynamics of infectious diseases when the host population is highly heterogenous.

Emphasis has been put in discussing our motivations and results in the context of influenza. Specifically, the role of cross-immunity and quarantine on the transmission dynamics of influenza within age-structured populations are studied. Thresholds, persistence, equilibria and their stability are found for models that include a quarantine class. For influenza type parameters, it was shown that periodic solutions can arise via Hopf bifurcation as the effectiveness of quarantine varies. The Hopf bifurcation surface and stable periodic solutions are found numerically. A system of delay differential equations modeling a fixed period of isolation is also studied. Conditions for the existence of periodic solutions and the possibility of stability switches are discussed for a distributed delay model. In addition, conditions that guarantee the local stability analysis of the disease-free steady-state distribution as well as the existence of an endemic steady-state distribution are established for SIQR (Susceptible-Infected-Quarantine-Recovered) models with age structure.