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Applied Mathematics Colloquium

Friday, October 21,  2005, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

Modeling Biological Invasions -- from beetles in New Jersey to plants in the Everglades

Gareth J. Russell

Department of Mathematical Sciences, Division of Biological Sciences, NJIT

and

Department of Biological Sciences

Rutgers, Newark

Abstract

I will describe a current research project that attempts to model the invasion dynamics of the Asian Long-Horned Beetle among the trees of New York City (and more recently, New Jersey). The data are characterized by uncertainty over the timing of infestation of individual trees, and of the period when they were 'contagious'. Our general approach is a likelihood model of the spread of a disease on a network of susceptible agents whose relationship is described by a graph. Particular models differ in how they assign transmission rates along edges of the graph. We incorporate timing uncertainty into the likelihood function by integrating expressions for the probability of infection over the ranges of uncertainty. Our first approach assumes that the uncertainties surrounding different events are independent, which is not true, but may be a reasonable approximation in the case of the Beetle. Finally, I will discuss future developments in terms of other systems (e.g., invading plants in Everglades National Park) and better models that incorporate contingency between events in the invasion process.