Math Colloquiums - Dr. Linda Allen

Mathematical Models for Two Emerging Diseases of Wildlife:
Hantavirus and Chytridiomycosis

Linda J. S. Allen
Department of Mathematics and Statistics
Texas Tech University
RH 249. Monday, March 19, 2007.  12.30 p.m.

Abstract: The emergence of new wildlife diseases and re-emergence of old diseases have been attributed to three processes: (i) ecosystem alterations, (ii) movement of pathogens or vectors, and (iii) changes in microbes or in the recognition of them. In this lecture, we highlight some of the wildlife emerging infectious diseases (EID) and factors associated with their emergence. We concentrate on two wildlife EID, hantavirus infection in rodents and chytrid infection in amphibians.

Hantavirus infections in rodents have emerged due to anthropogenic landscape changes and climatic changes that influence the reservoir host. Hantavirus is associated with the human EID hantavirus pulmonary syndrome (Fig. 1), identified in 1993 from an outbreak that occurred in New Mexico.

Figure 1. Transmission Dynamics of Hantavirus

Chytridiomycosis (Fig. 2) is a fungal infection of amphibians, identified in 1998 from dead and dying frogs in Australia and Panama. Emergence of this latter disease may be attributed to movement (global trade, use as laboratory animals) of infected amphibians around the world.

Figure 2. Number of Amphibian Species Infected with Chytrid

Mathematical modeling efforts (Fig. 3) for these two diseases will be discussed. Mathematical models and statistical analyses have helped interpret trends in the spread of these diseases,  provided greater understanding of underlying causes of outbreaks and have  provided guidance in the  collection of data towards further understanding.

Figure 3. Susceptible-Exposed-Infected-Recovered (SEIR) Model for Spread of Infection Among Males and Female.

This talk will be accessible to undergraduates.

Biographical Sketch:
Linda J. S. Allen received a B.A. degree in mathematics from the College of St. Scholastica in Duluth, Minnesota and M.S. and Ph.D. degrees in mathematics from the University of Tennessee in Knoxville. From 1982 to 1985, she was an assistant professor of mathematics at the University of North Carolina at Asheville. Dr. Allen came to Texas Tech University in 1985 and has been a Professor of Mathematics since 1998.

Dr. Allen's research specializations are mathematical biology and mathematical epidemiology. She develops, analyzes, and numerically simulates models that are applicable to a variety of biological systems. In particular, she has developed and analyzed models related to endangered water snakes, plant pathogens, cholla cacti, insect pests, and human and wildlife diseases (measles, chickenpox, chlamydia, hantavirus, and rabies). She is the author of two textbooks on deterministic and stochastic mathematical models in biology: ``An Introduction to Stochastic Processes with Applications to Biology'' and ``An Introduction to Mathematical Biology.''

Dr Linda Allen's Home Page