Journal of Advances In Allergy & Immunologic Diseases

ISSN: 2575-6184

VOLUME: 2 ISSUE: 1

OPTIMAL CONTROL MODEL FOR IMMUNE EFFECTORS RESPONSE AND MULTIPLE CHEMOTHERAPY TREATMENT (MCT) OF DUAL DELAYED HIV - PATHOGEN INFECTIONS


Citation

Bassey E. Bassey, OPTIMAL CONTROL MODEL FOR IMMUNE EFFECTORS RESPONSE AND MULTIPLE CHEMOTHERAPY TREATMENT (MCT) OF DUAL DELAYED HIV - PATHOGEN INFECTIONS(2017)SDRP Journal of Infectious Diseases Treatment & Therapy 1(1)

Abstract

In tackling the persistent menace of the deadly human immunodeficiency virus (HIV) and its accompanying acquired immunodeficiency syndrome (AIDS), some notably mathematical models have been formulated. In this present study, a number of compatible models were studied. The result of which led to the formulation of a classical 5-Dimensional delay-differential dynamic equations, principally primed with the investigation of the methodological application of multiple chemotherapy treatment (MCT) in the presence of delay intracellular and cell-mediated immune effectors response on the interplay of dual delayed HIV-pathogen infections and the T-lymphocytes cells. The model was presented as an optimal control problem and analyses conducted using classical numerical methods – Pontryagin’s minimum principle. The method demanded for the verification of positivity of state variables and boundedness of solution; as well as the establishment of model existence of optimal control pair for MCT and the system dynamic optimality solution. Using in-built Runge-Kutter of order of precision 4 in a Mathcad platform, the resulting analyses were subjected to numerical verification. Numerical simulations indicated that maximization of uninfected T-lymphocytes cells is dynamic under drug validity period. Importantly, the model established the fact that upperbounds on treatment optimal weight factors and presence of delay intracellular are crucial to the maximization of healthy CD4+ T cells, significant reduction of virions and suppression of infected CD4+ T cells. Furthermore, the rapid response of virions and infected cells to multiple chemotherapy treatment is emphatically attributed to the enormous role of boosted immune effectors response. The study therefore, advocate for a more accurate model that extensively define the role of the immune effectors response.

References

  1. Velichenko, V.V. and Pritykin, D. A. (2006) Numerical Methods of Optimal Control of the HIV-Infection Dynamics. Journal of Computer and Systems Sciences International, 45, No. 6, 894?905.

    View Article           

  2. Joshi, H. R. (2002) Optimal Control of an HIV Immunology Model. Optimal Control Applications and Methods, 23, 199-213.

    View Article           

  3. Butler, S., Kirschner, D. and Lenhart, S. (1995) Optimal Control of the Chemotherapy Affecting the Infectivity of HIV. Mathematical Biology and Medicine, World Scientic, 6, 557-569.

  4. Bassey, E. B., Kimbir, R.A. and Lebedev, K. A. (2016) On Optimal Control Model for the Treatment of Dual HIV-Parasitoid Pathogen Infection. J. Bioengineer & Biomedical Sci., 7: 212, 1-7, doi: 10.4172/2155-9538.1000212.

    View Article           

  5. Kirschner, D., Lenhart, S. and Serbin, S. (1997) Optimal control of the chemotherapy of HIV. J. Math. Biol., 35, 775-792. PMid:9269736

    View Article      PubMed/NCBI     

  6. Fister, K. R., Lenhart, S. and Mc Nally, J. S. (1998) Optimizing Chemotherapy in an HIV Model. Journal of Differential Equations, 32, 1-12.

  7. Kirschner D, Webb GF (1998) Immunotherapy of HIV-1 Infection. J. Biol. Syst., 6, 1, 71-83.

    View Article           

  8. Hattaf, K. and Yousfi, N. (2012) Two optimal treatments of HIV infection model. World Journal of Modelling and Simulation, 8, 1, 27-35.

  9. Zhu, H. and Zou, X. (2009) Dynamics of a HIV-1 infection model with cell-mediated immune response and intracellular delay. Discrete and continuous dynamical systems series B, 12, 2, 511?524.

    View Article           

  10. Hattaf, K. and Yousfi, N. (2012) Optimal Control of a Delayed HIV Infection Model with Immune Response Using an Efficient Numerical Method. Biomathematics, 2012, 1-7.

    View Article           

  11. Wang, K., Wang, W. and Liu, X. (2006) Global Stability in a viral infection model with lytic and nonlytic immune response. Computers and Mathematics with Applications, 51, 1593?1610.

    View Article           

  12. Hale, J. and Verduyn Lunel, S. M. (1993) Introduction to Functional Differential Equations. Applied Mathematical Science, 99, Springer-Verlag, New York.

    View Article           

  13. Perelson, S. A., Kirschner, E. D. and De Boer, R. (1993) Dynamics of HIV-infection of CD4+ T cells. Mathematical Biosciences, 114, 81-125. 90043-A

    View Article           

  14. Fleming, W. and Rishel, R. (1975) Deterministic and Stochastic Optimal Control. Springer Verlag, New York.

    View Article           

  15. Lukes, D. L. (1982) Differential Equations: Classical To Controlled, vol. 162 of Mathematics in Science and Engineering. Academic Press, New York, NY, USA.

  16. G?ollmann, L., Kern, D. and Maurer, H. (2009) Optimal control problems with delays in state and control variables subject to mixed control-state constraints. Optimal Control Applications and Methods, 30, 4, 341?365.

    View Article