Modeling population dynamics driven by external factors

Maria Leite
Mathematics and Statistics, University of Toledo

(November 19, 2013 10:20 AM - 11:15 AM)

Modeling population dynamics driven by external factors

Abstract

I will introduce mathematical models describing the influence of external factors in the temporal dynamics of populations. One model incorporates climate factors into the dynamics of seasonal influenza through three ecology-based response functions: response of influenza virus survival and human susceptibility to air temperature as well as influenza virus transmission response to specific humidity. I will discuss numerical simulation results obtained when the model are driven by temperature and specific humidity data. Interestingly, the models reproduce not only the reported double peaks of influenza A cases in subtropicalregion, but also the observed temporal pattern of flu in temperate regions (one winter peak).

Two other models incorporating the effect of insect outbreaks either as a single disturbance in the forest population dynamics or coupled with wildfire disturbances. The results show that 1) the beetle-tree system parameterized model exhibits the well known temporal dynamics of beetle-tree interaction described by the dual equilibria theory. 2) The beetle-tree-fire model reveals the existence of positive feedback between wildfire and insect outbreak disturbances in certain region of fire strength. This result agrees with one of the current theories in the field.