# American Institute of Mathematical Sciences

• Previous Article
Theoretical models for chronotherapy: Periodic perturbations in hyperchaos
• MBE Home
• This Issue
• Next Article
A method for analyzing the stability of the resting state for a model of pacemaker cells surrounded by stable cells
2010, 7(3): 527-552. doi: 10.3934/mbe.2010.7.527

## Rotating antibiotics selects optimally against antibiotic resistance, in theory

 1 Department of Mathematics, Imperial College London, SW7 2AZ, London, United Kingdom, United Kingdom

Received  September 2009 Revised  March 2010 Published  June 2010

The purpose of this paper is to use mathematical models to investigate the claim made in the medical literature over a decade ago that the routine rotation of antibiotics in an intensive care unit (ICU) will select against the evolution and spread of antibiotic-resistant pathogens. In contrast, previous theoretical studies addressing this question have demonstrated that routinely changing the drug of choice for a given pathogenic infection may in fact lead to a greater incidence of drug resistance in comparison to the random deployment of different drugs.
Using mathematical models that do not explicitly incorporate the spatial dynamics of pathogen transmission within the ICU or hospital and assuming the antibiotics are from distinct functional groups, we use a control theoretic-approach to prove that one can relax the medical notion of what constitutes an antibiotic rotation and so obtain protocols that are arbitrarily close to the optimum. Finally, we show that theoretical feedback control measures that rotate between different antibiotics motivated directly by the outcome of clinical studies can be deployed to good effect to reduce the prevalence of antibiotic resistance below what can be achieved with random antibiotic use.
Citation: Robert E. Beardmore, Rafael Peña-Miller. Rotating antibiotics selects optimally against antibiotic resistance, in theory. Mathematical Biosciences & Engineering, 2010, 7 (3) : 527-552. doi: 10.3934/mbe.2010.7.527
 [1] Urszula Ledzewicz, Heinz Schättler. Drug resistance in cancer chemotherapy as an optimal control problem. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 129-150. doi: 10.3934/dcdsb.2006.6.129 [2] Urszula Ledzewicz, Shuo Wang, Heinz Schättler, Nicolas André, Marie Amélie Heng, Eddy Pasquier. On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach. Mathematical Biosciences & Engineering, 2017, 14 (1) : 217-235. doi: 10.3934/mbe.2017014 [3] Cristian Tomasetti, Doron Levy. An elementary approach to modeling drug resistance in cancer. Mathematical Biosciences & Engineering, 2010, 7 (4) : 905-918. doi: 10.3934/mbe.2010.7.905 [4] Avner Friedman, Najat Ziyadi, Khalid Boushaba. A model of drug resistance with infection by health care workers. Mathematical Biosciences & Engineering, 2010, 7 (4) : 779-792. doi: 10.3934/mbe.2010.7.779 [5] Zhenzhen Chen, Sze-Bi Hsu, Ya-Tang Yang. The continuous morbidostat: A chemostat with controlled drug application to select for drug resistance mutants. Communications on Pure & Applied Analysis, 2020, 19 (1) : 203-220. doi: 10.3934/cpaa.2020011 [6] Nicolas Bacaër, Cheikh Sokhna. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Mathematical Biosciences & Engineering, 2005, 2 (2) : 227-238. doi: 10.3934/mbe.2005.2.227 [7] Ami B. Shah, Katarzyna A. Rejniak, Jana L. Gevertz. Limiting the development of anti-cancer drug resistance in a spatial model of micrometastases. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1185-1206. doi: 10.3934/mbe.2016038 [8] 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 [9] Urszula Ledzewicz, Heinz Schättler, Mostafa Reisi Gahrooi, Siamak Mahmoudian Dehkordi. On the MTD paradigm and optimal control for multi-drug cancer chemotherapy. Mathematical Biosciences & Engineering, 2013, 10 (3) : 803-819. doi: 10.3934/mbe.2013.10.803 [10] Arturo Alvarez-Arenas, Konstantin E. Starkov, Gabriel F. Calvo, Juan Belmonte-Beitia. Ultimate dynamics and optimal control of a multi-compartment model of tumor resistance to chemotherapy. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2017-2038. doi: 10.3934/dcdsb.2019082 [11] Divya Thakur, Belinda Marchand. Hybrid optimal control for HIV multi-drug therapies: A finite set control transcription approach. Mathematical Biosciences & Engineering, 2012, 9 (4) : 899-914. doi: 10.3934/mbe.2012.9.899 [12] Antonio Fernández, Pedro L. García. Regular discretizations in optimal control theory. Journal of Geometric Mechanics, 2013, 5 (4) : 415-432. doi: 10.3934/jgm.2013.5.415 [13] K. Renee Fister, Jennifer Hughes Donnelly. Immunotherapy: An Optimal Control Theory Approach. Mathematical Biosciences & Engineering, 2005, 2 (3) : 499-510. doi: 10.3934/mbe.2005.2.499 [14] Timothy C. Reluga, Jan Medlock, Alison Galvani. The discounted reproductive number for epidemiology. Mathematical Biosciences & Engineering, 2009, 6 (2) : 377-393. doi: 10.3934/mbe.2009.6.377 [15] K.F.C. Yiu, K.L. Mak, K. L. Teo. Airfoil design via optimal control theory. Journal of Industrial & Management Optimization, 2005, 1 (1) : 133-148. doi: 10.3934/jimo.2005.1.133 [16] Jacques Demongeot, Mohamad Ghassani, Mustapha Rachdi, Idir Ouassou, Carla Taramasco. Archimedean copula and contagion modeling in epidemiology. Networks & Heterogeneous Media, 2013, 8 (1) : 149-170. doi: 10.3934/nhm.2013.8.149 [17] Carlos M. Hernández-Suárez, Oliver Mendoza-Cano. Applications of occupancy urn models to epidemiology. Mathematical Biosciences & Engineering, 2009, 6 (3) : 509-520. doi: 10.3934/mbe.2009.6.509 [18] John Boscoh H. Njagarah, Farai Nyabadza. Modelling the role of drug barons on the prevalence of drug epidemics. Mathematical Biosciences & Engineering, 2013, 10 (3) : 843-860. doi: 10.3934/mbe.2013.10.843 [19] Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control & Related Fields, 2012, 2 (2) : 195-215. doi: 10.3934/mcrf.2012.2.195 [20] Laurenz Göllmann, Helmut Maurer. Theory and applications of optimal control problems with multiple time-delays. Journal of Industrial & Management Optimization, 2014, 10 (2) : 413-441. doi: 10.3934/jimo.2014.10.413

2018 Impact Factor: 1.313