Optimization of the force exerted by the synergistic treatment-immune response interaction
Optimización de la fuerza ejercida por la interacción sinérgica tratamiento-respuesta inmunitaria
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In physics, synergy is an action that involves the coordination of two or more causes or parts, whose effects will be greater than the sum of the individual effects. Measuring the synergistic strength of the treatment and the immune response working together is of vital importance to control physicochemical parameters in bacterial infections. In this sense, in this article we focus on analyzing the impact of synergy through an optimal control problem. To formulate and solve the problem we use conservation laws that characterize the main properties of the physical phenomenon. Specifically, we use the Pontryagin Minimum Principle to minimize a performance functional that measures the strength of the synergy between treatment and immune response. The numerical results suggest that the forces synergies must be proportional to each other to control bacterial spread.
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Ankomah, P., & Levin, B. R. (2014). Exploring the collaboration between antibiotics and the immune response in the treatment of acute, self-limiting infections. Proceedings of the National Academy of Sciences of the United States of America, 111(23), 8331–8338. https://doi.org/10.1073/PNAS.1400352111/SUPPL_FILE/PNAS.201400352SI.PDF DOI: https://doi.org/10.1073/pnas.1400352111
Handel, A., Margolis, E., & Levin, B. R. (2009). Exploring the role of the immune response in preventing antibiotic resistance. Journal of Theoretical Biology, 256(4), 655–662. https://doi.org/10.1016/J.JTBI.2008.10.025 DOI: https://doi.org/10.1016/j.jtbi.2008.10.025
Ibargüen-Mondragón, E., & Esteva, L. (2013). On the interactions of sensitive and resistant Mycobacterium tuberculosis to antibiotics. Mathematical Biosciences, 246(1), 84–93. https://doi.org/10.1016/J.MBS.2013.08.005 DOI: https://doi.org/10.1016/j.mbs.2013.08.005
Ibargüen-Mondragón, E., Esteva, L., & Cerón Gómez, M. (2022). An optimal control problem applied to plasmid-mediated antibiotic resistance. Journal of Applied Mathematics and Computing, 68(3), 1635–1667. https://doi.org/10.1007/S12190-021-01583-0 DOI: https://doi.org/10.1007/s12190-021-01583-0
Ibargüen-Mondragón, E., Prieto, K., & Hidalgo-Bonilla, S. P. (2021). A MODEL ON BACTERIAL RESISTANCE CONSIDERING A GENERALIZED LAW OF MASS ACTION FOR PLASMID REPLICATION., 29(2), 375–412. https://doi.org/10.1142/S0218339021400118 DOI: https://doi.org/10.1142/S0218339021400118
Ibargüen-Mondragón, E., Romero-Leiton, J. P., Esteva, L., Cerón Gómez, M., & Hidalgo-Bonilla, S. P. (2019). Stability and periodic solutions for a model of bacterial resistance to antibiotics caused by mutations and plasmids. Applied Mathematical Modelling, 76, 238–251. https://doi.org/10.1016/J.APM.2019.06.017 DOI: https://doi.org/10.1016/j.apm.2019.06.017
Landersdorfer, C. B., Ly, N. S., Xu, H., Tsuji, B. T., & Bulitta, J. B. (2013). Quantifying subpopulation synergy for antibiotic combinations via mechanism-based modeling and a sequential dosing design. Antimicrobial Agents and Chemotherapy, 57(5), 2343–2351. https://doi.org/10.1128/AAC.00092-13/SUPPL_FILE/ZAC999101813SO1.PDF DOI: https://doi.org/10.1128/AAC.00092-13
Leung (Joey), C. Y., & Weitz, J. S. (2017). Modeling the synergistic elimination of bacteria by phage and the innate immune system. Journal of Theoretical Biology, 429, 241–252. https://doi.org/10.1016/J.JTBI.2017.06.037 DOI: https://doi.org/10.1016/j.jtbi.2017.06.037
Lowden, J., Miller Neilan, R., & Yahdi, M. (2014). Optimal control of vancomycin-resistant enterococci using preventive care and treatment of infections. Mathematical Biosciences, 249(1), 8–17. https://doi.org/10.1016/J.MBS.2014.01.004 DOI: https://doi.org/10.1016/j.mbs.2014.01.004
Massad, E., Burattini, M. N., & Coutinho, F. A. B. (2008). An optimization model for antibiotic use. Applied Mathematics and Computation, 201(1–2), 161–167. https://doi.org/10.1016/J.AMC.2007.12.007 DOI: https://doi.org/10.1016/j.amc.2007.12.007
Ortega Bejarano, D. A., Ibarguen-Mondragon, E., & Gomez-Hernandez, E. A. (2018). A stability test for non linear systems of ordinary differential equations based on the Gershgorin circles. Contemporary Engineering Sciences, 11(91), 4541–4548. https://doi.org/10.12988/CES.2018.89504 DOI: https://doi.org/10.12988/ces.2018.89504
Udekwu, K. I., & Weiss, H. (2018). Pharmacodynamic considerations of collateral sensitivity in design of antibiotic treatment regimen. Drug Design, Development and Therapy, 12, 2249–2257. https://doi.org/10.2147/DDDT.S164316 DOI: https://doi.org/10.2147/DDDT.S164316
