Event Type:

Mathematical Biology Seminar

Date/Time:

Wednesday, November 9, 2011 - 08:00 to 09:00

Location:

STAG 222

Event Link:

Local Speaker:

Abstract:

There are several ecological examples that suggest that the outcome of competition between two or more species can possibly be changed in the presence of a pathogen that affects both the species leading to invasion of native species by exotic,

non-native species. We formulate and analyze new stochastic models based on continuous time Markov chains and stochastic differential equations that account for the variability in births and deaths due to competitive interactions among multiple host species and the variability in the transmission process when a common pathogen is spread among these hosts. A system of ordinary differential equations for n competing species with a shared pathogen serves as the deterministic skeleton for the stochastic formulations. Analytical results about pathogen persistence or extinction are summarized for the deterministic model for two and three species. Then we present some new results about stability of the infection-free state and the possibility of one species invading a system of n − 1 species. Lastly, we present numerical simulations that explore the effect of disease

on two species competition and illustrate some of the analytical results and highlight some of the differences in the stochastic and deterministic models.