Effect of optimal linear control in human monocytes and macrophages system

  • María Aracelia Alcorta García
  • Yosefat Nava Alemán
  • Nora Elizondo Villarreal
  • Facundo Cortés Martínez
  • Ernesto Torres López
  • Sonia G. Anguiano Rostro
  • Luis Gerardo Garza


Monocytes M and macrophages Mϕ cells are mononuclear essential components of the innate immune system response. M and Mϕ are mononuclear phagocytes that have crucial roles in tissue homeostasis and innate immunity. M Are key players during inflammation and pathogen challenge also are precursor of Mϕ, whereas tissue resident Mϕ has important functions in development, tissue homeostasis and the resolution of inflammation. In previous work, linear optimal control equations with tracking in x2(t) (this is Mϕ) and control only in x1(t), (this is M) were applied obtaining good results. In this work, Linear Optimal Control equations for states x1(t) and x2(t), with tracking in the state x2(t) were applied. It is possible to obtain better convergence results of the states to the asymptotic values (healthy state) when the production rate of (M) and λ into the state equations was modified. Tables and graphics are included.


1. Stewart James and Day Troy, Bio calculus, Calculus for the Life Sciences, Ed. Cengage Learning, Boston MA, USA, 2015, 662-670.
2. Vargas De León Cruz, Modelo Biomatematico de la dinámica de Infección del Virus del Dengue, Revista Alternativa, Colombia, 2005, 6, 1-32.
3. Onoja Matthew Akpa and Benjamin Agboola Oyejola, Modeling the transmission dynamics of HIV/AIDS epidemics: an introduction and review, J Infect Dev Ctries, USA, 2010, 4 (10), 597-608.
4. KEELING MATT J., KEN T. D. EAMES, Networks and epidemic models, The Royal Society, Interface, United Kingdom, 2008, 295-307.
5. Anderson, Hakan, Britton, Tom, Stochastic Epidemic Models and their Statistical Analysis, Springer Lecture Notes in Statistics, USA, 2000, 151.
6. R. Bellman, Dynamic Programming. Dover, Princeton, New Jersey, USA, 2003.
7. L. S. Pontryagin, The Mathematical Theory of Optimal Processes, Wiley Interscience, USA, 1962.
8. KALMAN R. E., The Theory of Optimal Control and the Calculus of Variations, Mathematical Optimization Techniques, R. E. Bellman, Santa Monica: The RAND Corporation, California, USA, 1963.
9. Kalman R. E., Mathematical Description of linear Dynamical Systems, J SIAM Control, Series A, 1963, 152-192.
10. Kalman R. E., Contributions to the Theory of Optimal Theory, Boletin de la Sociedad Matematica Mexicana, México, 1960, 2, 102-119.
11. Kirk Donald E., Optimal Control Theory, Dover, Mineola, New York, USA, 2004.
12. Arthur E. Bryson, Applied Linear Optimal Control, Cambridge, United Kingdom, 2002.
13. Ma. Aracelia Alcorta García, Yosefat Nava Alemán, Nora Elizondo Villarreal, Facundo Cortés Martínez, Ernesto Torres López, Sonia Gpe. Anguiano Rostro, Optimal Control Effect into Innate Immune System, proceedings of ICMEAE 2015. IEEEXplorer, ISBN: 978-14-4673-8329-5/15, DOI: 10.1109/ICMEAE.2015.19. Cuernavaca, Morelos México, 2015.
14. Fahy RJ, Doseff AI, Wewers MD, Spontaneous human monocyte apoptosis utilizes a caspase-3-dependent pathway that is blocked by endotoxin and is independent of caspase-1., J Immunol., USA. 1999, 1755-1762, 163 (4).
15. Wiktor-Jedrzejczak W, Gordon S., Cytokine regulation of the macrophage (M phi) system studied using the colony stimulating factor1-deficient op/op mouse, Physiol Rev., USA, 1996, 927-947, 76.
16. Sepulveda Saabedra J., Texto Atlas de Histología, Biología Celular y Tisular, Mc Graw Hill, México D. F., 2012.
17. Arti Parihar, Timothy D. Eubank, Andrea I. Doseff, Monocytes and Macrophages Regulate immunity through Dynamic Networks of Survival and Cell Death, Journal of Innate Immunity, Switzerland, 2010, 3, 204-215,
18. Auffray C., Sieweke M.H., Geissmann F., Review Blood monocytes: development, heterogeneity, and relationship with dendritic cells, Annu Rev Immunol, Lafayette, IN, 2009, 27, 669-692.
19. Linker R, Gold R, Luhder F, Review Function of neurotrophic factors beyond the nervous system: inflammation and autoimmune demyelination, Crit. Rev. Immunol., Danbury, CT 06810, 2009, 29(1), 43-68.
20. T. Ganz, R. I. Leher, Chapter 88. Production, distribution and fate of monocytes and macrophages, in William's Hematology, McGraw Hill, New York, USA, 1995, 875-878, 5.
21. Y. Goto, et al, Anovel method to quantify the turnover and release of monocytes from the bone marrow using the thymidine analog 5'-bromo-2'-dexoyuridine, Am J Physiol Cell Physiol, Bethesda, MD 20814, 2003, pp. C253-C259, 28(5).
22. MICR3453: The Mathematical Theory of Optimal Processes. http://www.utep.edu/eerael/immunology.htm, 1998.
23. F. Ginhoux, S. Jung, Monocytes and macrophages: developmental pathways and tissue homeostasis, Nature Reviews Immunology, N. Y., USA, 2014, 14, 392-404.
24. W. S. Levine, The Control Handbook, A CRC Handbook Published in Cooperation with IEEE Press. Florida, USA, 1995, 760-763. http://www.crcpress.com

How to Cite
GARCÍA, María Aracelia Alcorta et al. Effect of optimal linear control in human monocytes and macrophages system. Journal of Bioengineering Science, [S.l.], v. 1, n. 1, p. 1-11, july 2017. Available at: <https://www.archyworld.com/journals/index.php/jbs/article/view/98>. Date accessed: 16 june 2019. doi: https://doi.org/10.22496/jbs.v1i1.98.