For more information about this meeting, contact Andrew Belmonte, Hope Shaffer.

Title: | The optimal path to epidemic extinction |

Seminar: | Seminar on Mathematics in the Bio and Geo Sciences |

Speaker: | Eric Forgoston, Dept of Mathematical Sciences, Montclair State University |

Abstract: |

The control and eradication, or fade-out, of infectious diseases
is an important goal for improving public health. In order to enhance
methods of disease control, including vaccination and social group
quarantine, one must first 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. From
a probabilistic viewpoint, these dynamics can change the probability of
extinction. In large, finite populations, the extinction of an infectious
disease epidemic is a rare event. We will show that the process of
extinction proceeds along an optimal path which maximizes the probability of
disease fade-out. Moreover, we will show that the optimal path also
possesses a maximal sensitivity to initial conditions, which can be
quantified by computing finite-time Lyapunov exponents. As a result, the
optimal path emerges naturally from the underlying dynamical system and may
be constructed explicitly using the finite-time Lyapunov exponents. The
theory will be applied to several stochastic epidemiological models. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 10 / 19 / 2011 |

Time: | 01:00pm - 02:00pm |