Iranian Journal of Biomedical Engineering (IJBME)
نشریه علمی مهندسی پزشکی زیستی

Robust Linear Controller Design for Uncertain Malaria Epidemic Model

Document Type : Full Research Paper

Authors

Hamed Hanifi 1
Elham Amini Boroujeni 2

1 M.Sc., Department of Electrical and Computer Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

2 Assistant Professor, Department of Electrical and Computer Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

https://doi.org/10.22041/ijbme.2024.2026160.1895
Abstract
This paper aims to design a robust linear controller to prevent a malaria epidemic as an ascending system with an uncertain model. The prevalence of malaria is modeled together by seven nonlinear differential equations for population variables: susceptible, susceptible, infected, and improved humans, and susceptible, exposed, and infected mosquitoes. The robust controllers are designed to adjust the use of treated beds properly, the treatment rate of infected people, and the use of insecticide spray to control the malaria epidemic. Accordingly, using the designed control scheme, the number of exposed and infected humans and infected mosquitoes will eventually reach zero. However, the number of susceptible and susceptible mosquitoes is increasing due to the birth rate and the loss of malaria immunity in the improved population. This article describes the methods (H2, H∞-ric, H∞-lmi, H2-H∞, μD-K, μD-G-K). We have tried to control this disease's prevalence despite the system's uncertainty. Finally, the results of the reduced-order controllers are evaluated and compared, and the best-designed controller is compared with one of the recent research on this subject. The results are shown in the simulation section.

Keywords

Malaria
Epidemiological
Robust Control
Uncertain Model
Decrease Rank
Subjects
  1. Caccetta L., Foulds, L.R., Rumchev V.G.; A positive linear discrete-time model of capacity planning and its controllability properties. Math. Comput. Model., 2004, 40, pp. 217–226.
  2. Zhang, J., Jia, X., Zhang, R., et al.: A model predictive control framework for constrained uncertain positive systems. Int. J. Syst. Sci., 2018, 49, (4), pp. 884–896.
  3. Brauer, F.: ‘Some simple epidemic models’, Math. Biosci. Eng., 2006, 3, (1), pp. 1–15.
  4. Arino, J., Brauer, F., van den Driessche, P., etal.: ‘A model for influenza with vaccination and antiviral treatment’, J. Theor. Biol., 2008, 253, (1), pp. 118–130.
  5. Pathak, S., Maiti, A., Samanta, G.P.: ‘Rich dynamics of an SIR epidemic model’, Nonlinear Anal., Model. Control, 2010, 15, (1), pp. 71–81.
  6. World Health Organization: ‘World malaria report 2015’, World Health Organization, 2016.
  7. Beare, N.A.V., Taylor, T.E., Harding, S.P., et al.: ‘Malarial retinopathy: a newly established diagnostic sign in severe malaria’, Am. J. Trop. Med. Hyg., 2006, 75, (5), pp. 790–797.
  8. Cowman, A.F., Berry, D., Baum, J.: ‘The cellular and molecular basis for malaria parasite invasion of the human red blood cell’, J. Cell Biol., 2012, 198, (6), pp. 961–971.
  9. Ross, R.: ‘The prevention of malaria’ (John Murray, London, 1911).
  10. Blayneh, K., Cao, Y., Kwon, H.D.: ‘Optimal control of vector-borne diseases: treatment and prevention’, Discrete Continuous Dyn. Syst. B., 2009, 11, (3), pp. 587–611.
  11. Li, X.-J., Yang, G.-H.: ‘Robust adaptive fault-tolerant control for uncertain linear systems with actuator failures’, IET Control Theory Applic., 2012, 6, (10), pp. 1544–1551.
  12. Moghaddam, A.V., Rajaei, A., Vatankhah, R., et al.: ‘Terminal sliding mode control with non-symmetric input saturation for vibration suppression of electrostatically actuated nanobeams in the presence of Casimir force’, Appl. Math. Model, 2018, 60, pp. 416–434.
  13. Torabi, M., Sharifi, M., Vossoughi, G.: ‘Robust adaptive sliding mode admittance control of exoskeleton rehabilitation robots’ Sci. Iran., 2018, 25, (5), pp. 2628–2642.
  14. Rajaei, A., Vahidi-Moghaddam, A., Ayati, M., et al.: ‘Integral sliding mode control for nonlinear damped model of arch microbeams’, Microsyst. Technol., 2019, 25, (1), pp. 57–68.
  15. Vahidi-Moghaddam, A., Rajaei, A., Ayati, M.: ‘Disturbance-observer-based fuzzy terminal sliding mode control for MIMO uncertain nonlinear systems’, Appl. Math. Model, 2019, 70, pp. 109–127.
  16. Sharifi, M., Moradi, H.: ‘Nonlinear robust adaptive sliding mode control of influenza epidemic in the presence of uncertainty’, J. Process Control, 2017, 56, pp. 48–57.
  17. Amiri Mehra, A. H., Zamani, I., Abbasi, Z., Ibeas, A., Observer-based adaptive PI sliding mode control of developed uncertain SEIAR influenza epidemic model considering dynamic population, Journal of Theoretical Biology, 2019, 482, 109984.
  18. Aghajanzadeh, O., Sharifi, M., Falsafi, A., Robust control strategy for HBV treatment: Considering parametric and nonparametric uncertainties, Academic Press: Control Applications for Biomedical Engineering Systems , 2020, pp. 127-147.
  19. Okosun K.O., Rachid, O., Marcus, N.: ‘Optimal control strategies and costeffectiveness analysis of a malaria model’, Biosystems, 2013, 111, (2), pp. 83–101.
  20. Rajaei A.; Vahidi-Moghaddam, A.; Chizfahm, A.; Sharifi, M. Control of malaria outbreak using a non-linear robust strategy with adaptive gains. IET Control Theory Appl.2019, 13, 2308–2317.
  21. Zhou, J. C. Doyle; Essentials of Robust Control, Prentice Hall, 1999.
  22. دکترحمیدرضا تقی­راد، محمد فتحی، فرینا زمانی اسگویی. کنترل مقاوم H∞، انتشارات دانشگاه خواجه نصیر الدین طوسی، تهران،نوبت چاپ سوم،
Iranian Journal of Biomedical Engineering (IJBME)
Volume 17, Issue 4
Winter 2024
Pages 315-329

  • Receive Date 07 April 2024
  • Revise Date 23 August 2024
  • Accept Date 05 October 2024

Home

Contact Us