CONTRIBUTED SESSION 4 317 Contributed Session 04: Modelling and Math Biology Oscillations in epidemic models: the role of infection and recovery times Guillermo Abramson Instituto Balseiro - Centro Atomico Bariloche, Ar- gentina abramson@cab.cnea.gov.ar Sebastian Gon¸ calves, Marcelo F. C. Gomes Traditional epidemic models consider that individual processes occur at constant rates. That is, an in- fected individual has a constant probability per unit time of recovering from infection after contagion. This assumption certainly fails for almost all infec- tious diseases, in which the infection time usually follows a probability distribution more or less spread around a mean value. We show a general treatment for an SIRS model in which both the infected and the immune phases admit such a description. The general behavior of the system shows transitions be- tween endemic and oscillating situations that could be relevant in many real scenarios. The interaction with the other main source of oscillations, seasonal- ity, will also be discussed. -! 1⇧1 - Optimal vaccine procurement strategy for smallpox epidemic Burcu Adivar Izmir University of Economics, Turkey burcu.ozcam@ieu.edu.tr Ebru Selin Selen In this study, epidemiological modeling is used to develop optimal order policy for vaccine require- ments for an anticipated epidemic or pandemic at- tack. Based on a compartmental model for the dis- persion of smallpox virus, we consider vaccination as the main control policy in addition to hospitaliza- tion and quarantine. Solution to a set of ordinary differential equations is used to estimate the need for vaccines for two different population sizes. As- suming zero initial stock level for smallpox vaccines, we propose a minimum cost vaccine procurement strategy by determining optimal order quantity and order timing to stop the dispersion of epidemic as early as possible. Dynamic programming is used to solve the single commodity inventory model under deterministic time varying demand rate. -! 1⇧1 - Can activation of latently infected cells reduce the size of the HIV reservoir? Stanca Ciupe Virginia Tech, USA stanca@vt.edu Jon Forde, Joseph Volpe While antiretroviral drugs can drive HIV to un- detectably low levels in the blood, eradication is hindered by the persistence of long-lived, latently infected memory CD4 T cells. Immune activation therapy aims to eliminate this latent reservoir by reactivating these memory cells, exposing them to removal by the immune system and the cytotoxic effects of active infection. In this paper we develop a mathematical model that investigates the use of immune activation strategies while limiting virus and latent class rebound. Our model considers infection of two memory classes, central and transitional CD4 T cells and the role that general immune activation therapy has on their elimination. Further, we in- corporate ways to control viral rebound by blocking activated cell proliferation through anti proliferation therapy. Using the model we provide insight into the control of latent infection and subsequently into the long term control of HIV infection. -! 1⇧1 - The stability analysis and impact of predator mortality rate on age-structured models Michael Cowen University of North Carolina Wilmington, USA mtc9565@uncw.edu Wei Feng, Shana Johnson This paper analyzes the effects of an age-structured prey-predator system where the prey has two stages, juvenile and adult. Three different models are used to evaluate the benefits of this structure with regards to predator mortality rate and stability of the sys- tem. We assessed how various parameters for prey growth rate and death rate affected each model and we determined necessary conditions for stability in all cases. The focus of this paper is to find the condi- tions necessary to ensure asymptotic stability of the equilibrium point where both the predator and prey can co-exist. More specifically, we demonstrate how the importance of predator mortality rate changes in each system. -! 1⇧1 -