DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Ira Schwartz, Naval Research Laboratory

**Title: ***
The Dynamical Geometry of Epidemic Extinction
*

**Abstract:**
The control and eradication, or fade-out, of infectious diseases
is a penultimate goal for improving public health. In order to
promote and design control methods, such as vaccination and
social group quarantine, one must determine how the disease
spreads dynamically. However, modeling the dynamics of an
outbreak includes many complicating features, such as
deterministic and stochastic chaotic-like behavior. Such
complicated dynamics can enhance the probability of extinction.
In large populations, although extinction occurs with probability
one, extinction is considered a rare event which maximizes the
probability of disease fade-out.

In this talk, we show that the path to extinction possesses a maximal sensitivity to initial conditions which is similar to local measures of chaotic behavior, and may be quantified by computing finite time Lyapunov exponents. As a result, the extinction path emerges naturally from the underlying dynamical geometry and may be constructed explicitly. The theory will be applied to several stochastic epidemiological models.

This work is done in collaboration with Drs. Eric Forgoston,
Simone Bianco, and Leah Shaw, and is supported by the Office of
Naval Research, National Institutes of Health, and Air Force Office of
Scientific Research.

**Time:** Friday, Oct. 28, 2011, 1:30-2:30 p.m.

**Place:** Science and Tech I, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491