# American Institute of Mathematical Sciences

2014, 11(6): 1449-1464. doi: 10.3934/mbe.2014.11.1449

## A mathematical model for antibiotic control of bacteria in peritoneal dialysis associated peritonitis

 1 Department of Mathematics and Statistics, California State University, Holt Hall 181, Chico, CA 95929 2 Departments of Critical Care Medicine and Medicine, University of Pittsburgh and Pittsburgh Veterans Affairs Healthcare System, 644A Scaife Hall, 3550 Terrace Street, Pittsburgh, PA, 15261, United States 3 Departments of Critical Care Medicine and Medicine, University of Pittsburgh Pittsburgh Veterans Affairs Healthcare System, 644A Scaife Hall, 3550 Terrace Street, Pittsburgh, PA, 15261, United States

Received  November 2013 Revised  September 2014 Published  September 2014

A study of the process of pharmacokinetics-pharmacodynamics (PKPD) of antibiotics and their interaction with bacteria during peritoneal dialysis associated peritonitis (PDAP) is presented. We propose a mathematical model describing the evolution of bacteria population in the presence of antibiotics for different peritoneal dialysis regimens. Using the model along with experimental data, clinical parameters, and physiological values, we compute variations in PD fluid distributions, drug concentrations, and number of bacteria in peritoneal and extra-peritoneal cavities. Scheduling algorithms for the PD exchanges that minimize bacteria count are investigated.
Citation: Colette Calmelet, John Hotchkiss, Philip Crooke. A mathematical model for antibiotic control of bacteria in peritoneal dialysis associated peritonitis. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1449-1464. doi: 10.3934/mbe.2014.11.1449
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