Abstract
We develop a mathematical framework to model the dynamics of the effect of antimicrobial agents on heterogeneous microbial populations of distributed antimicrobial resistance. Our framework uses the concept of cumulants of a distribution. Simplifications that result in easily usable approximation tools are presented. A case study on experimental data exemplifies shortcomings of standard methods and the usefulness of the proposed approach. Suggestions for future development are made.
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Cohen, M.L.: Epidemiology of drug-resistance - implications for a postantimicrobial era. Science 257, (5073), 1050–1055 (1992)
Craig, W.A.: Pharmacokinetic/pharmacodynamic parameters: Rationale for antibacterial dosing of mice and men. Clinical Infectious Diseases 26, 1–12 (1998)
Drlica, K.A.: Strategy for fighting antibiotic resistance. ASM News 67, (1), 27–33 (2001)
Giraldo, J., Vivas, N.M., Vila, E., Badia, A.: Assessing the (a)symmetry of concentration-effect curves: Empirical versus mechanistic models. Pharmacology& Therapeutics 95, 21–45 (2002)
Gold, H.S., Moellering, R.C.: Antimicrobial-drug resistance. N. Engl. J. Med. 335, 1444–1453 (1996)
Hill, A.V.: The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J. Physiol. 40 (iv-vii), (1910)
Jusko, W.: Pharmacodynamics of chemotherapeutic effects: Dose-time-response relationships for phase-nonspecific agents. J. Pharm. Sci. 60, 892–895 (1971)
Levy, S.B.: The challenge of antibiotic resistance. Scientific American (1998)
Lipsitch, M., Levin, B.R.: The population dynamics of antimicrobial chemotherapy. Antimicrobial Agents and Chemotherapy 41, 2, 363–373 (1997)
Morens, D.M., Folkers, G.K., Fauci, A.S.: The challenge of emerging and re-emerging infectious diseases. Nature 430, 08 July, 242–249 (2004)
Mueller, M., de la Peña, A., Derendorf, H.: Issues in pharmacokinetics and pharmacodynamics of anti-infective agents: Kill curves versus mic. Antimicrobial Agents and Chemotherapy, 48 (2), 369–377 (2004)
Neu, H.C.: The crisis in antibiotic resistance. Science, 257, 1064–1073 (1992)
Robertson, T.B.: The chemical basis of growth and senescence. Lippincott, Philadelphia, 1923
Tam, V., Schilling, A., Melnick, D., Coyle, E.: Comparison of beta-lactams in counter-selecting resistance of pseudomonas aeruginosa. Diagn Microbiol Infect Dis, 52 (2), 145–151 (2005)
Varaldo, P.E.: Antimicrobial resistance and susceptibility testing: An evergreen topic. Journal of Antimicrobial Chemotherapy, 50, 1–4 (2002)
Wagner, J.: Kinetics of pharmacologic response i. Proposed relationships between response and drug concentration in the intact animal and man. J. Theoret. Biol. 20, 173–201 (1968)
Weisstein, E.W.: Cumulant. http://mathworld.wolfram.com/Cumulant.html
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Nikolaou, M., Tam, V. A New Modeling Approach to the Effect of Antimicrobial Agents on Heterogeneous Microbial Populations. J. Math. Biol. 52, 154–182 (2006). https://doi.org/10.1007/s00285-005-0350-6
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DOI: https://doi.org/10.1007/s00285-005-0350-6