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

Title: | Dynamics of an epidemic model with non-local infections for diseases with latency over a patchy environment |

Seminar: | The Pritchard Lab Seminar |

Speaker: | Jing Li, Dept of Mathematics, Penn State |

Abstract: |

In this talk, with the assumptions that an infectious disease in a
population has a fixed latent period and the latent individuals of the
population may disperse, we formulate an SIR model with a simple demographic
structure for the population living in an n-patch environment (cities,
towns, or countries, etc.). The model is given by a system of delay
differential equations with a fixed delay accounting for the latency and a
non-local term caused by the mobility of the individuals during the latent
period. Assuming irreducibility of the travel matrices of the infection
related classes, an expression for the basic reproduction number R0 is
derived, and it is shown that the disease free equilibrium is globally
asymptotically stable if R0 < 1, and becomes unstable if R0 > 1. In the
latter case, there is at least one endemic equilibrium and the disease will
be uniformly persistent. When n = 2, two special cases allowing reducible
travel matrices are considered to illustrate joint impact of the disease
latency and population mobility on the disease dynamics. In addition to the
existence of the disease free equilibrium and interior endemic equilibrium,
the existence of a boundary equilibrium and its stability are discussed for
these two special cases. |

### Room Reservation Information

Room Number: | MB315 |

Date: | 09 / 20 / 2010 |

Time: | 02:30pm - 03:30pm |