### Mathematical Biosciences and Engineering

2014, Issue 6: 1449-1464. doi: 10.3934/mbe.2014.11.1449

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

• Received: 01 November 2013 Accepted: 29 June 2018 Published: 01 September 2014
• MSC : Primary: 92C35, 92C45, 92C50, 92C60; Secondary: 92B05, 92C05.

• 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[J]. Mathematical Biosciences and Engineering, 2014, 11(6): 1449-1464. doi: 10.3934/mbe.2014.11.1449

### Related Papers:

• 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.

 [1] Clin. Drug. Invest., 11 (1996), 229-239. [2] Clin. Infect. Dis., 15 (2002), 1212-1218. [3] Lippincott Williams & Wilkins, 2011. [4] Antimicrobial Agents Chemotherapy, 47 (2003), 3764-3767. [5] Adv. Exp. Med. Biol., 696 (2011), 401-410. [6] ASAIO Journal, (2004), 568-576. [7] Peritoneal Dialysis International, 22 (2002), 339-344. [8] in The Textbook of Peritoneal Dialysis, Kluwer Academic Publishers, 1994, 135-160. [9] Peritoneal Dialysis International, 11 (1991), 252-260. [10] Pharmacol. Rev., 65 (2013), 1053-1090. [11] Antimicrob. Agents & Chemo., 48 (2004), 3670-3676. [12] Lippincott Williams & Wilkins, 2006. [13] J. Pharm. Sci., 75 (1986), 1063-1067.
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