IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Ninth Annual Graduate Student Mini-conference in Computational Mathematics

Chayu Yang
University of Tennessee, Chattanooga
Abstract

On the intrinsic dynamics of bacteria in waterborne infections

  • Feb. 17, 2018
  • 2:20 p.m.
  • LeConte 412

The intrinsic dynamics of bacteria often play an important role in the transmission and spread of waterborne infectious diseases. In this paper, we construct mathematical models for waterborne infections and analyze two types of nontrivial bacterial dynamics: logistic growth, and growth with Allee effects. For the model with logistic growth, we find that regular threshold dynamics take place, and the basic reproduction number can be used to characterize disease extinction and persistence. In contrast, the model with Allee effects exhibits much more complex dynamics, including the existence of multiple endemic equilibria and the presence of backward bifurcation and forward hysteresis.

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