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Optimal control of treatments in a two-strain tuberculosis model
| 1. | Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6367, United States |
| 2. | Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, United States |
| 3. | Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395, United States |
| [1] |
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 |
| [2] |
Cristiana J. Silva, Helmut Maurer, Delfim F. M. Torres. Optimal control of a Tuberculosis model with state and control delays. Mathematical Biosciences & Engineering, 2017, 14 (1) : 321-337. doi: 10.3934/mbe.2017021 |
| [3] |
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 |
| [4] |
Yali Yang, Sanyi Tang, Xiaohong Ren, Huiwen Zhao, Chenping Guo. Global stability and optimal control for a tuberculosis model with vaccination and treatment. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 1009-1022. doi: 10.3934/dcdsb.2016.21.1009 |
| [5] |
Eduardo Ibarguen-Mondragon, Lourdes Esteva, Leslie Chávez-Galán. A mathematical model for cellular immunology of tuberculosis. Mathematical Biosciences & Engineering, 2011, 8 (4) : 973-986. doi: 10.3934/mbe.2011.8.973 |
| [6] |
Mudassar Imran, Hal L. Smith. A model of optimal dosing of antibiotic treatment in biofilm. Mathematical Biosciences & Engineering, 2014, 11 (3) : 547-571. doi: 10.3934/mbe.2014.11.547 |
| [7] |
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 |
| [8] |
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 |
| [9] |
Eduardo Ibargüen-Mondragón, Lourdes Esteva, Edith Mariela Burbano-Rosero. Mathematical model for the growth of Mycobacterium tuberculosis in the granuloma. Mathematical Biosciences & Engineering, 2018, 15 (2) : 407-428. doi: 10.3934/mbe.2018018 |
| [10] |
Shuo Wang, Heinz Schättler. Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1223-1240. doi: 10.3934/mbe.2016040 |
| [11] |
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 |
| [12] |
Cristiana J. Silva, Delfim F. M. Torres. Optimal control strategies for tuberculosis treatment: A case study in Angola. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 601-617. doi: 10.3934/naco.2012.2.601 |
| [13] |
Juan Pablo Aparicio, Carlos Castillo-Chávez. Mathematical modelling of tuberculosis epidemics. Mathematical Biosciences & Engineering, 2009, 6 (2) : 209-237. doi: 10.3934/mbe.2009.6.209 |
| [14] |
Clara Rojas, Juan Belmonte-Beitia, Víctor M. Pérez-García, Helmut Maurer. Dynamics and optimal control of chemotherapy for low grade gliomas: Insights from a mathematical model. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1895-1915. doi: 10.3934/dcdsb.2016028 |
| [15] |
Maciej Leszczyński, Urszula Ledzewicz, Heinz Schättler. Optimal control for a mathematical model for anti-angiogenic treatment with Michaelis-Menten pharmacodynamics. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2315-2334. doi: 10.3934/dcdsb.2019097 |
| [16] |
Michele L. Joyner, Cammey C. Manning, Whitney Forbes, Michelle Maiden, Ariel N. Nikas. A physiologically-based pharmacokinetic model for the antibiotic ertapenem. Mathematical Biosciences & Engineering, 2016, 13 (1) : 119-133. doi: 10.3934/mbe.2016.13.119 |
| [17] |
Urszula Ledzewicz, Behrooz Amini, Heinz Schättler. Dynamics and control of a mathematical model for metronomic chemotherapy. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1257-1275. doi: 10.3934/mbe.2015.12.1257 |
| [18] |
Cecilia Cavaterra, Denis Enăchescu, Gabriela Marinoschi. Sliding mode control of the Hodgkin–Huxley mathematical model. Evolution Equations & Control Theory, 2019, 8 (4) : 883-902. doi: 10.3934/eect.2019043 |
| [19] |
Elena Fimmel, Yury S. Semenov, Alexander S. Bratus. On optimal and suboptimal treatment strategies for a mathematical model of leukemia. Mathematical Biosciences & Engineering, 2013, 10 (1) : 151-165. doi: 10.3934/mbe.2013.10.151 |
| [20] |
Expeditho Mtisi, Herieth Rwezaura, Jean Michel Tchuenche. A mathematical analysis of malaria and tuberculosis co-dynamics. Discrete & Continuous Dynamical Systems - B, 2009, 12 (4) : 827-864. doi: 10.3934/dcdsb.2009.12.827 |
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