American Institute of Mathematical Sciences

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July  2007, 8(1): 127-143. doi: 10.3934/dcdsb.2007.8.127

The dynamics of bacterial infection, innate immune response, and antibiotic treatment

Mudassar Imran 1, and  Hal L. Smith 2,

1. 

Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, United States
2. 

Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, 85287, United States

Received  October 2006 Revised  November 2006 Published  April 2007

We develop a simple mathematical model of a bacterial colonization of host tissue which takes account of nutrient availability and innate immune response. The model features an infection-free state which is locally but not globally attracting implying that a super-threshold bacterial inoculum is required for successful colonization and tissue infection. A subset $B$ of the domain of attraction of the disease-free state is explicitly identified. The dynamics of antibiotic treatment of the infection is also considered. Successful treatment results if the antibiotic dosing regime drives the state of the system into $B$.
Keywords: infection., Pharmacokinetics, pharmacodynamics, antibiotic treatment.
Mathematics Subject Classification: Primary: 92C50,92C45 ; Secondary: 34C9.
Citation: Mudassar Imran, Hal L. Smith. The dynamics of bacterial infection, innate immune response, and antibiotic treatment. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 127-143. doi: 10.3934/dcdsb.2007.8.127
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